March 01, 2025
Posted by Karachi Board Notes
March 01, 2025
Posted by Karachi Board Notes
March 01, 2025
Posted by Karachi Board Notes
May 17, 2014
Posted by Karachi Board Notes
Electrostatics
2nd Year Physics Notes
karachiboardnotes.blogspot.com
ELECTROSTATICS
State and Explain Coulomb's Law.
INTRODUCTION
In 1974, Sir Augusts de coulomb studied the relationship between
localized charges. He carried out experiments using torsion balance. In
the basis of his experimental results, he proposed a law known as
Coulomb's Law.
Statement
The electric force of interaction between two point charges is directly
proportional to product of their charges and inversely proportional to
the square of the distance from their centers.
Mathematical Expression
Consider two points charges q1 and q2 and let "1" be the separation between them. According to Coulomb's Law.
F ∞ q1 q2 -------- (i)
And, according to second part
F ∞ 1/r² --------- (ii)
Combining eq (i) and eq (ii), we get
F ∞ q1 q2 / r²
F = K q1 q2 / r²
Where K is the constant of proportionality and its value depends upon
the medium between the two charges. In S.I system its value is equal to
K = 8.98 x 10(9) N-m² / c².
Coulomb's Law can be expressed in terms of permitivity as follows.
F = 1 / 4 π Є . q1 q2 / r²
Where Єo is the permitivity of free space and its value is
Єo = 8.85 x 10(-12) col² / Nm²
if some other medium is used instead of air then
F = 1 / 4 π Єo Єr . q1 q2 / r²
Where Єr is the relative permitivity which is different for different dielectric.
Define electric field and electric intensity. Find the formula for the electric intensity due to a point charge.
ELECTRIC INTENSITY
DEFINITION
Electric intensity is the force experienced by a unit positive charge due to the presence of a charge body.
EXPLANATION
It is the measure of the strength of the electric field. Electric
intensity is a vector quantity and its direction is same as that of
force. If the charge is positive then electric intensity is directed
from the charge and if the charge is negative, then it is directed
towards the charge. The SI unit of electric intensity is Newton per
Coulomb or volt per meter.
Mathematical Form
Mathematically electric intensity is given by
E = F / q°
Where E = Electric Intensity
F = Force
q° = small magnitude
ELECTRIC INTENSITY DUE TO A POINT CHARGE
CONSIDERATION
Consider a charged body q that has an electric field all around it. We
want to find out electric intensity E at point P. For this purpose, we
placed a point charge q1 at that point.
Define Electric flux. Find the formula for the electric flux due to point charge in a closed sphere.
ELECTRIC FLUX
DEFINITION
The total number of imaginary lines drawn in such a way that the
attraction of tangent at any point is same as that of electric field
crossing a surface normally is called electric flux or flux on the
surface.
OR
The total number of lines of forces crossing a surface normally is called flux on that surface.
Mathematical Form
The flux at a surface is determined by the product of flux density i.e.
electric field and the projection of its area perpendicular to the field
or by the product of area and component of field normal to the area.
ELECTRIC FLUX DUE TO A POINT CHARGE IN A CLOSED SPHERE
Consider an isolated point charge +q. Th lines of forces from q will
spread uniformly in space around it cutting the surface of an imaginary
sphere. Now we want to find flux due to point charge. For this purpose,
we divide the whole sphere into small patches. Each patch is denoted by
ΔA.
State and prove Guass's Law
The total electric flux diverging out from a closed surface is equal to
the product of the sum of all charges present in that closed surface and
1/ Єo.
Find the Formula for Electric Intensity.
1. Due to Charge Sheet
2. Due to Two Charge Sheets
OR
What are the application of Guass's Law.
Introduction
Guass's Law can be used to calculate the electric field only in those
cases of charge distribution which are so symmetrical that by proper
choice of Guassian surface the flux on it may possibly be evaluated.
With the help of guass's law we can measure the intensity in following
cases.
1. Electric Intensity due to charge sheet.
2. Electric Intensity due to two charge sheets.
1. Electric Intensity Due to Charge Sheet.
Consider a charge sheet in which unit positive charges are uniformly distributed.
As we know that charge density is the charge stored per unit area and is denoted by
σ = Q / A
=> Q = σ A
According to Guass's Law
σ = Q / Є
=> φe = σ A / Є -------- (I)
Now consider a cylindrical shell, which is placed inside the charge sheet. It has three surfaces.
* Upper Surface
* Curve Surface
* Bottom
Electric Intensity Due to Upper Surface
φ1 = E ΔA
φ1 = E ΔA cos θ
But θ = 0° and cos 0° = 1, therefore,
φ1 = E ΔA cos 0°
= φ1 = E ΔA
Electric Intensity Due to Curved Surface
φ2 = E ΔA
φ2 = E ΔA cos θ
Since the angle between the field vector and area vector of all elements of curved surface is 90°, therefore,
φ2 = E ΔA cos 90°
But cos 90° = 0,
φ2 = E ΔA (0)
φ2 = 0
Electric Intensity Due to Lower Surface
φ3 = E ΔA
φ3 = E ΔA cos θ
But 0 = 0° and cos 0°, = 1 therefore,
φ3 = E ΔA cos 0°
=> φ3 = E ΔA
Total Flux
Total Flux is given by
φe = φ1 + φ2 + φ3
=> φe = E ΔA + 0 + E ΔA
=> φe = 2E ΔA
For the whole charge sheet:
=> φe = 2E Σ ΔA
=> φe = 2 EA ----------- (II)
Comparing equation (I) and (II)
=> σ A / Єo = 2AE
=> E = σ / 2 Єo
OR
E = σ / 2 Єo
2. Electric Intensity Due to Two Charge Sheets.
As we know that electric intensity due to a charge sheet is
E = σ / 2 Єo
For two sheets E will be,
=> E = σ / 2 Єo + σ / 2 Єo
=> E = σ + σ / 2 Єo
=> E = 2 σ / 2 Єo
=> E = σ / Єo
=> E = σ / Єo i
Define the term Capacitor and Capacitance of a Capacitor
CAPACITOR
Capacitor is a device which is use to storage charge. A simple capacitor
consists of two parallel metallic plates. A plate is connected to the
positive terminal of the battery and another plate is connected to the
negative terminal of the battery.
CAPACITANCE
Definition
The capacity of a capacitor to store the charge is known as Capacitance.
Mathematical Explanation
If V is the voltage provided to the capacitor and Q is the amount of
charge stored in the capacitor, then it is observed that if more is the
voltage, then more will be the charge stored in the capacitor.
Mathematically,
Q ∞ V
=> Q = CV
Where C is the capacitance of the capacitor which may be defined as
The ratio of the charge on one of the plate (conductor) to the potential difference between them.
Unit of Capacitance
The unit of Capacitance is Farad. It may be defined as,
If one coulomb charge is stored due to 1 volt potential, then capacitance will be 1 Farad.
Factors on which Capacitance Depends.
The Capacitance of a capacitor depends upon following factors.
1. Cross-sectional area of plate
2. Separation between plates
3. Dielectric
On the basis of dielectric capacitors are classified into different
types. For example Electrolyte Capacitor, Paper Capacitor, Meca
Capacitor, Oil Capacitor.
Types of Capacitor
There are two main types of Capacitors.
1. Fixed Capacitor
2. Variable Capacitor
1. Fixed Capacitor
Those capacitor whose capacitance is constant are known as Fixed Capacitor. For example Paper Capacitor and Meca Capacitor.
2. Variable Capacitor
Those capacitor whose capacitance is not fixed are known as Variable Capacitor. For example Gang Capacitor.
Find the Formula for the capacitance of Parallel plate capacitor.
PARALLEL PLATE CAPACITOR
Definition
A parallel plate capacitor is a device used to store the charge. It
consist of two parallel metallic plates. A plate is connected to the
positive terminal of the battery and another plate is connected to the
negative terminal of the battery. These plates are separated by a very
small distance compared to the dimension of the plates.
CAPACITANCE OF A PARALLEL PLATE CAPACITOR
Consideration
Consider a parallel plate capacitor in which is the distance between the
plates the charge stored is denoted by Q where as potential difference
between the plates is V.
Derivation of the Formula
As we known that electric intensity due to two charge sheets is
E = σ / Єo
Since charge density is given by
σ = Q / A
Substituting the value in above equation
E = Q / A Єo --------- (I)
According to the definition of electrical potential.
ΔV = E Δ
Substituting the value of E from eq (I) in above equation
Q = C x Qd / A Єo
C = A Єo / d
If some other medium is used instead of air then,
C = A Єo Єr / d
Find the formula for equivalent capacitance when,
1. Capacitors are connected in Series
2. Capacitors are connected in Parallel
Introduction
Capacitors of some fixed values are used in a circuit. The capacitance
of the desired value can however be obtained by suitable combination of
capacitor. Capacitors can be combined in parallel, series or both.
WHEN CAPACITORS ARE CONNECTED IN SERIES OR SERIES COMBINATION
Consideration
Consider three capacitors having capacitance C1, C2, C3 connected in a
series. These capacitors can be replace by an equivalent capacitor
having capacitance Ce. When a cell is connected across the ends of
system then a charge Q is transferred across the plates of capacitors. A
charge upon one plate always attracts upon the other plate with a
charge equal in magnitude and opposite in sign.
Let V be the potential difference across the combination. The potential
difference across the individual capacitor is Vab, Vbc, Vcd.
Derivation of the Formula
As we know that in case of series combination the charge across the
individual capacitor remains constant, where as potential difference
varies such that the potential difference V is the sum of potential
difference applied across individual capacitor.
Vad = Vab + Vbc + Vcd ------------ (I)
We know that,
Q = CV
V = Q / C
Therfore,
Vad = Q / Ce
Vab = Q / C1
Vbc = Q / C2
Vcd = Q / C3
Substituting the values of Vad, Vab, Vbc and Vcd in eq (I)
Q/Ce = Q/C1 + Q/C2 + Q/C3
Q/Ce = Q [1/C1 + 1/C2 + 1/C3]
1/Ce = 1/C1 + 1/C2 + 1/C3
Conclusion
The reciprocal of the equivalent capacitance is equal to the sum of the reciprocals of the individual capacitance.
WHEN CAPACITORS ARE CONNECTED IN PARALLEL OR PARALLEL COMBINATION
Consideration
Consider three capacitors having C1, C2, C3 capacitance respectively are
connected in parallel. We can replace them by an equivalent capacitor
having capacitance Ce. A charge q given to a point divide it self reside
on the plates of individual capacitor as Q1, Q2, Q3 respectively.
Derivation of the Formula
As we known that in case of parallel combination the potential
difference across each capacitor is that of the source where as the
charge across each capacitor varies, therefore the total charge Q is
given by
Q = Q1 + Q2 + Q3 --------- (I)
As we known that,
Q = CV
Therefore,
Q = Ce Vab
=> Q1 = C1 Vab
=> Q2 = C2 Vab
=> Q3 = C3 Vab
Substituting the values of Q1, Q2, Q3 in eq (I)
Ce Vab = C1 Vab + C2 Vab + C3 Vab
Ce Vab + Vab (C1 + C2 + C3)
Ce = C1 + C2 + C3
Conclusion
The equivalent capacitance is equal to sum of the individual capacitances.
Define electric potential and absolute potential.
ELECTRIC POTENTIAL
Definition
Electric Potential is the amount of work done in order to bring a unit
positive charge from one point to another point against the direction of
electric field.
Explanation
In order to bring a unit positive charge from one point to another
point, we have to do some work. This work is stored in the form of
potential energy. This potential energy per unit charge is known as
Electric Potential.
Mathematical Form
Electric Potential is denoted by V. It is defined as the potential energy per unit charge. Therefore mathematically,
ΔV = Δu / q ------- (I)
We know that
Δu = F. Δr
But E = F/q => F = Eq, therefore,
Δu = EqΔr
Substituting the value in eq (I)
ΔV = EqΔr / q
=> ΔV = E. Δr
Where,
ΔV = Electric Potential
E = Electric Intensity
Δr - Displacement
From above expression we know that
Electric Potential is the dot product of electric intensity and displacement.
It is a scalar quantity and its unit is Volt.
ABSOLUTE POTENTIAL
Definition
Absolute potential is the amount of work done in order to bring a unit
positive charge from one point to infinite distance against the
direction of magnetic field.
ELECTRIC POTENTIAL
Electric Potential is the amount of work done in order to move a unit
positive charge from one point to another against the direction of
electric.
Consideration
Consider a unit positive charge placed in a uniform electric field. We
have to displace it from point O to point N. For this purpose we have to
do some work. This work is known as electric potential. In order to
determine electric potential from point O to point N we divide the whole
distance into small equal patches because in a long distance intensity
does not remain constant. This patch is denoted by Δr
Electrostatics 2nd Year Physics Notes karachiboardnotes.blogspot.com ELECTROSTATICS State and Explain Coulomb's Law. INTRODUCTION In...
May 17, 2014
Posted by Karachi Board Notes
Current electricity
2nd Year Physics Notes
karachiboardnotes.blogspot.com
CURRENT ELECTRICITY
Define Charge and Current.
CHARGE
Definition
Flow of electron is known as Charge.
It is denoted by Q.
Unit
Its unit is Coulomb.
1 Coulomb = 10(-6) μcoulomb
1 coulomb = 10 (-3) mili coulomb
1 coulomb = 10(-9) neno coulomb
CURRENT
Definition
The flow of charge per unit time is known as Current.
It is denoted by I.
Unit
The unit of current is coulomb/sec or Ampere.
AMPERE
If one coulomb charge passes through the conductor in 1 second then the current is 1 Ampere.
Mathematical Form
Mathematically,
I = Q/t
State and Explain Ohm's Law.
OHM'S LAW
Introduction
A German scientist George Simon Ohm studied the relationship between
voltage, current and resistance. On the basis of his experimental
results, he proposed a law which is known as Ohm's Law.
Statement
Ohm's Law to metallic conductors can be stated as
The current through a conductor is directly proportional to the
potential difference between the ends of the conductor provided that
physical conditions are kept constant.
It can also be stated as
The ratio between voltage and current remains constant, if the physical conditions are kept constant.
Mathematical Form
Mathematically,
V ∞ I
V = IR
R = V/I
Where R is the constant of proportionality known as resistance of the
conductor. Its unit is volt per ampere (Volt/Ampere) or Ohm (Ω).
Ohm (Ω)
If 1 ampere current passes through the conductor due to 1 volt potential difference then the resistance of conductor is 1 Ohm.
Resistance
Opposition offered in the flow of current.
Graphical Representation.
When graph is plotted between current and potential differences then straight line is obtained.
Limitations of the Law
Ohm's Law is valid only for metallic resistance at a given temperature and for steady currents.
Define the term Resistivity or Coefficient of Resistor.
RESISTIVITY OR COEFFICIENT OF RESISTOR
Definition
It is the resistance of a unit conductor whose cross-sectional area is 1 sqm.
Unit
Its unit is Ohm meter.
Mathematical Form
The resistance of any conductor depends upon the following factors.
1. Length of the conductor
2. Cross-sectional area of the conductor.
3. Material of the conductor.
The resistance of the conductor is directly proportional to the length
of the conductor and inversely proportional to the cross-sectional area.
Mathematically,
R ∞ L -------- (I)
R α 1/A ------ (II)
Combining eq (I) and (II)
R α L/A
=> R = ρL/A
Where ρ is the constant of proportionality known as Resistivity or Coefficient of resistance.
ρ = RA/L
Explain the effect of temperature on resistance or temperature coefficient of resistance.
EFFECT OF TEMPERATURE ON RESISTANCE
It is observed that if we increase the temperature then resistance of a conductor will increase.
Consideration
Let Ro be the initial resistance of a conductor at 4°C. If we increase
the temperature from t1°C to t2°C, then resistance will increase. This
increment in resistance is denoted by ΔR. The increment in resistance
depends upon the following two factors.
1. Original Resistance (Ro)
2. Difference in temperature Δt.
Mathematical Verification
The increment in resistance is directly proportional to the original resistance and temperature difference.
Mathematically,
ΔR ∞ Ro ----- (I)
ΔR ∞ Δt ----- (II)
Combining eq (I) and eq (II) we get
ΔR ∞ RoΔt
=> ΔR = αRoΔt
Where α is the temperature coefficient of resistance. It is defined as
It is the increment in resistance per unit resistance per degree rise in temperature.
Its unit is 1/°C or °C. If RT is the total resistance, then
RT = Ro + ΔR
=> RT = Ro + αRo Δt
=> RT = Ro (1 + αΔt)
As we know that resistance is directly proportional to resistivity therefore,
ρT = ρo (1 + αΔt)
Define the term Power Decipation in Resistor.
POWER DECIPATION IN RESISTORS
Definition
When current flows in a conductor then a part of electrical energy
appears in the form of heat energy which is known as Power Decipation in
Resistor.
Units
Its unit is Joule per second (J/s). Most commonly used unit is Kwh.
1 Kwh = 36 x 10(5) Joules
Mathematical Form
Since,
P = Electrical Work / Time
Electrical Work = QV ------ (I)
This electrical work produces heat energy in the resistor.
P = QV / t
P = Q / t . V
But,
I = Q / t
P = VI
From Ohm's Law
V = IR
P = IIR
P = I2R
OR,
P = 12R2 / R
=> P = V2 / R
As we know that,
Energy = Power x time
=> E = P x t
=> E = Vit
=> E = I2Rt
And,
E = V2 / R . t
Define and explain Electromotive Force.
ELECTROMOTIVE FORCE
Definition
It is the terminal voltage difference when no current draws from a cell or a battery.
OR
Work done per coulomb on the charges.
It is denoted by E.
Unit
Electromotive force or simply e.m.f is a scalar quantity it has the same
dimension as that of voltage, therefore its unit is volt.
Explanation
When an electric current passes through a resistor, it dissipates
energy, which is transformed into heat energy. Thus to sustain a current
in conductor some source of energy is needed so that it could
continuously supply power equal to that which is dissipated as heat in
the resistor. The strength of this source is called Electromotive Force.
Consideration
Let consider a simple circuit in which a resistor "R" is connected by
leads of negligible resistance to the terminals of a battery. The
battery is made up of some electrolyte and electrode for the production
of e.m.f and hence when this current flows from battery, it encounters
some resistance by the electrolyte present in two electrodes. This
resistance is known as internal resistance "r" of the battery.
Mathematical Form
According to Ohm's Law
V = IR
I = V / R
Or,
I = E / R + r
Where E is e.m.f and r is internal resistance
=> E = IR + Ir
E = V + Ir
Current electricity 2nd Year Physics Notes karachiboardnotes.blogspot.com CURRENT ELECTRICITY Define Charge and Current. CHARGE Definition F...
May 17, 2014
Posted by Karachi Board Notes
Electrical measuring instruments
2nd Year Physics Notes
karachiboardnotes.blogspot.com
ELECTRICAL MEASURING INSTRUMENTS
THE MOVING COIL GALVANOMETER
The moving coil galvanometer is a basic electrical instrument. It is used for the detection or measurement of small currents.
Principle
When current flows in a rectangular coil placed in a magnetic field it
experience a magnetic torque due to which it rotates through an angle
proportional to the current flowing through it.
Construction:
The essential parts of a moving coil galvanometer are
1. A U-shaped permanent magnet with cylindrical concave pole-pieces.
2. A flat coil of thin enamel Insulated wire (usually rectangular)
3. A soft iron cylinder
4. A scalar lamp and scale arrangement.
In suspended type or D Arsonvals galvanometer the flat rectangular coil
of thin enamel insulated wire of suitable number of terms wound on a
light non-metallic or non-magnetic (brass or aluminum) frame is
suspected between the cylindrical concave pole pieces of the permanent
U-shaped magnet by a thin phosphor-bronze strip. One end of the wire of
the soil is soldered to strip. The other end of the strip is fixed to
the frame of the galvanometer and connected to an external terminal. It
serves as one current lead. The other end of the wire of the coil is
soldered to a loose and soft spiral of wire connected to another
external terminal. The soft spiral of wire serves as the other current
lead. A soft iron cylinder, coaxial with the pole-pieces is placed
within the frame of the coil but quite detached from it and is fixed to
the body of the galvanometer. In the space between it and the pole
pieces, where the coil moves freely, the soft iron cylinder makes the
field stronger and radial so that the magnetic field is always parallel
to the plane of the coil. To note the deflection a concave mirror along
with lamp and scale arrangement is used.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
Working
When a current passes through the galvanometer coil, it experiences a
magnetic deflecting torque, which tends to rotate it from its rest
position. As the coil rotates it produces a twist in the suspension
strip. The coil rotate until the elastic restoring torque due to which
the strip does not equalize and cancel the deflecting magnetic torque
and then it attains equilibrium and stops rotating further.
i.e. Deflecting torque = Restoring torque
But deflecting torque = BINA Cos α
BINA Cos α = c0
Where B = strength of the magnetic field
I = current in the coil
A = Area of the coil
N = Number of turns in the coil
θ = Angle of twist of the suspension strip
c = torque per unit twist of the suspension strip for the equilibrium
As c/BNA is constant.
In pivoted type or Weston galvanometer the coil instead or being
suspended by a strip is pivoted between two jeweled bearings. The
restoring torque is provided two hair springs one on either side of the
coil and curling on the opposite sense are connected one to each
spring. The hairspring thus also serve as current leads to the coil. A
light aluminum pointer is fixed to the coil, which moves over a
calibrated circular scale with equal divisions, which measures the
deflection directly.
Current Sensitivity of a Galvanometer
A galvanometer is said to be sensitive if for a small current the
deflection "θ" is sufficiently large. A galvanometer can be made more
sensitive if c/BNA is made small. Thus to increase sensitivity "c" may
be decreased or B, N and A may be increased "C" can be decreased by
increasing the length of suspension wire or by decreasing its can be
decreased by increasing the length of suspension wire or by decreasing
its diameter, but this process cannot be taken too far < as the
suspension must be strong enough to carry the coil. "N" or "A" cannot be
increased because it makes the coil heavy. The loss of sensitivity due
to the use of fewer turns is however made us by the very high value of
the magnetic field employed.
The current sensitivity of a galvanometer is usually defined as the
current in microampere required to cause one-millimeter deflection on a
scale place 1.0 meter from the mirror of the galvanometer.
THE AMMETER
Ammeter is an instrument, which is used for measuring electric
current. A galvanometer can measure small current if its scale is
calibrated for the current. For the measurement of large current a
bypass resistance called a shunt, of appropriate small value is
connected in parallel with the galvanometer coil. This resistance allows
the large excess current through itself while a fraction of the
current passes through the galvanometer coil. The scale of the
instrument is so calibrated that it can measure the main current
directly.
Consider a galvanometer "G" whose resistance is "Rg" and which gives
full scale deflection when current "Ig" flows through it to convert the
galvanometer into an ammeter which can measure a maximum current "I" a
shunt "Rs" of appropriate small resistance should be connected in
parallel with the galvanometer such that the current "Ig" must flow
through the galvanometer coil.
The potential difference "Vg" across the galvanometer is given by
Vg = Ig Rg
The potential difference "Vs" across the shunt is given by
Vs = Is Rs = (I - Ig) Rs
Where Is = I - Ig = current through the shunt.
As "Rg" and "Rs" are connected in parallel to each other therefore potential difference across them will be equal i.e.
Vs = Vg
(I - Ig) Rs = Ig Rg
Rs = Ig Rg / I - Ig
Ammeter is always connected in series with the circuit.
Multi Range Ammeter
Sometimes an ammeter has more than one range, which means that it has
as many different shunts as the ranges. The desired range is selected
by insertion the proper shunt in position. In one type, one end of each
shunt is permanently connected to a common terminal while the other
end of each is connected through a range to a second common terminal.
THE VOLTMETER
Voltmeter is an instrument which is used for measuring potential
difference between any two points of a current carrying (or between the
two terminals of a source of emf). A galvanometer can be used for
measuring a very small Potential Difference. If its scale is calibrated
for voltage. For the measurement of large potential difference. A high
resistance of the order of Kilo-ohms is connected in series with it.
This resistance is commonly known as "Multiplier Resistance".
Consider a galvanometer "G" where resistance is "Rg" and which deflects
full scale for the current "Ig" to convert this galvanometer into a
voltmeter measuring a Potential difference upto "V" volts. An
appropriate high resistance "Rn" must be connected in series with it
such that for the potential difference "V" applied between the ends of
the above combination. The current "Ig" must flow through the
galvanometer. However the total resistance between the terminal a & b
is Rn + Rg.
(Rn + Rg+ Ig = V
Rn + Rg = V / Ig
Rn = V / Ig - Rg
Voltmeter is always connected in parallel with the circuit.
Multirange Voltmeter
Sometimes a voltmeter has more than one range, which means it has as
many different resistance as the ranges. The desired range is selected
by inserting the proper resistance in position.
We have a common terminal marked (+) and as many other terminals as the
ranges. In the other type one terminal is common marked (+) while the
different range terminals can be connected by a range switch to the
other common terminals.
WHEAT STONE BRIDGE
If four resistances R1, R2, R3 and R4 are connected end to end in
order to form a closed mesh ABCDA and between one pair of opposite
junctions. A and C cell is connected through a key K1 while between the
pair of opposite junctions B and D a sensitive galvanometer "G" is
connected through another key K2. The circuit so formed is called a
"Wheatstone-bridge".
In the above bridge if the key is closed first, some current flows
through the cell and the resistance R1, R2, R3 and R4. If the key K2 is
also closed the current will usually be found to flow through the
galvanometer indicated by its deflection. However if the resistance R1,
R2, R3 and R4 (or at least one of them) are adjusted, a condition can
always be attached in which the galvanometer show no deflection at all
i.e. no current passes through it. Then the potential difference between
B & D must be zero i.e. B & D must be at the same potential.
This implies that
P.d. between A and B = p.d. between A and D
OR
V(AB) = V(AD)
P.d. between B and C = p.d. between D and C
OR
V(bt) = V(Dt)
Since no current flows through the galvanometer the current R1 equals
that in R2, say II and the current in R3 equals that in R4 say 12
As,
V(AB) = V(AD)
1(1) R(1) = 1(2) R(3) -------- (I)
Also,
V(BC) = V(DC)
1(1) R(2) = 1(2) R(4) --------- (II)
Dividing eq 1 by eq 2
1(1) R(1) / 1(1) R(1) = 1(1) R(1) / 1(1) R(1)
R(1) / R(1) = R(1) / R(1)
Under balanced condition if any three resistance are known then the fourth can be found easily (i.e. wheatstone principle).
The wheatstone principle is used in Meter Bridge, the P.O. box Carey Foster's Bridge, Callender and Graffite's Bridge etc.
METER BRIDGE
The Meter Bridge also called slide - Wire Bridge is an instrument
based on wheatstone principle. It consists of a long thick copper strip
bent twice at right angles. Two small portions are cut off from it near
the bends to provide the gaps across which two resistances are known
one and an unknown may be connected. Each of the three pieces of the
strip is provided with binding screws. A uniform wire (of magnetic or
other) one meter long and of fairly high resistance is stretched, along
the side a meter scale is connected to the ends of the strip.
For measuring an unknown resistance "X" it is connected in one gap of
the Meter Bridge and a standard resistance box "R" is connected in the
other gap. A cell and a galvanometer are connected. The jockey "J" is
moved along the wire to obtain the balance point D. Under balanced
condition if the length of the wire segment. A D toward X is Lx and the
length of the wire segment CD towards R is L(R) then their
resistances are ρL(R) respectively.
Where ρ = resistance per unit length of the wire.
POST OFFICE BOX [P.O BOX]
Post Office Box is an instrument, which is based on wheatstone
principle. It was first introduced for finding resistance of telegraph
wires and for fault - findings work in the post and telegraph office
that's why it is called "Post Office Box". It is more compact and easier
to use.
It consists of three sets of resistances P, Q and R. The arms P and Q
called the ratio arms, usually consists of three resistances each viz.
10, 100 and 1000 ohms so that any decimal ratio from 1:100 to 100:1 may
be used. The third arm "R" is an ordinary set of resistances. The
unknown resistances "X" to be measured forms the fourth arm. Introducing
the ratios 1:1, 10:1, 100:1 in turn the balance or null position is
traced by adjusting "R". Balance is usually obtained at the ratio 100:1
for some value of "R". With this value of "R" the value of X can be
easily be calculated using relation of Wheatstone bridge i.e.
P/Q = R/X
X = R Q/P
THE OHMMETER
The ohmmeter is a device used for the measurement of resistance. It
consists of a sensitive galvanometer "G", adjustable resister "R" and a
torch cell "E" connected in series between two terminals A and B. The
unknown resistance "X" to be measured is connected between the terminals
A and B. The resistance R is so chosen that when the terminals A and B
are short circuited (i.e. X = 0). The galvanometer gives full-scale
deflection when no connection is between A and B (i.e. X = ∞). The
galvanometer shows zero deflection for the value of X between = and ∞.
The deflection is small or large depending on the value of X. The scale
of the galvanometer is calibrated with different known values of X and
there the circuit serves as an ohmmeter to measure any unknown
resistance approx. The scale of the ohmmeter however is not linear.
Using different conditions of R is series and different shunts across
the galvanometer worked by range switches, the ohmmeter can be adopted
for different accessories for e.g. 1 Ω accuracy in tens of ohms, in
hundreds of ohms, in thousands of ohms, in mega ohms etc. Ohmmeter is
not a very accurate instrument.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
POTENTIOMETER
Potentiometer is device for measuring the p.d (voltage) between two
points of a circuit or the e.m.f of a current source. It consists of a
uniform wire stretched on a wooden board along a meter scale.
Consider a uniform resistance wire AB of length L and Resistance R,
across which is connected to a source of constant EMF (e.g. an
accumulator) through a key and a rheostat to adjust and maintain a
constant current 1 through it.
As the current flows, the P.d. between A and B = V(AB) = IR
If one terminal of a wire is connected to A while other is moved on the wire AB then instrument acts as a Potential Divider.
To find an unknown EMF of a cell or some other potential difference or
the ratio of the emf of two cells consider the circuit. The positive
terminals of a cell of unknown EMF "E(N)" and a standard cell of Emf
E(N) are connected to the terminal A. The negative terminals of both
the cells are joint to the jockey through a two way key and a sensitive
galvanometer. Using the two-way key first cell E(N) only is introduced
into the galvanometer branch and balanced point C and length L are
found for it.
THE AVO-METER
An Avo-meter is an apparatus which is used to measure current, voltage
and resistance in other words it is an ampere, volts and ohms. It can
measure direct as well as alternative voltage and currents. It consists
of a galvanometer with different scales graduated in such a way that
all the three quantities can be measured. A selector-cum-range switch
is provided. Its has its own battery. A rectifier is also included in
the instrument to convert A.C. into D.C. before they pass through the
Galvanometer
Electrical measuring instruments 2nd Year Physics Notes karachiboardnotes.blogspot.com ELECTRICAL MEASURING INSTRUMENTS THE MOVING C...
May 17, 2014
Posted by Karachi Board Notes
Advent of modern physics
2nd Year Physics Notes
karachiboardnotes.blogspot.com
ADVENT OF MODERN PHYSICS
What are the basic postulates of Einstein's Special theory of relativity. Also give the consequences of the theory.
EINSTEIN'S SPECIAL THEORY OF RELATIVITY
Introduction
Einstein examine the motion of objects in frames of references moving
relative to one another. On the basis of his experimental results he
proposed a special theory of relativity in the year 1905. This theory
is valid specially for inertial frames and is to be modified into a
general theory for accelerated frames of reference.
BASIC POSTULATES
The Einstein's special theory of relativity is based on two
assumptions known as the postulates of special relativity. The two
postulates are states as follows.
First Postulate
The speed of light was regarded as the universal constant. It means
that the speed of light in vacuum is the same for all observers in
uniform transnational motion and is independent of the motion of the
observer and the source.
Second Postulate
According to this postulate the laws of physics in the frame moving
with uniform velocity can be expressed by a single set of mathematical
expression.
This postulate points out if some event takes place in any of the frame
and the frames are moving with uniform velocity the result of the two
frames will be identical. Conversely if the frames are in accelerated
motion then the result will not be identical.
MASS ENERGY RELATION
Einstein proved that energy has inertia, which is the property of
matter and associated with mass. Thus mass is simply a property
attributed to the total energy of the body and only total energy is
required to know total mass of the body. Hence in special theory of
relativity total energy and mass are related by the famous Einstein's
equation.
E = mc(2)
From this relation between mass and energy it has been predicted that
any process that changed the mass by a detectable amount of energy.
Write a note on Compton Effect
COMPTON EFFECT
In 1926, Arthur Compton studies this phenomenon of change in
wavelength. On the basis of his experimental results he proposed a
theory based on the idea of photon theory of radiation. Since the
detailed study of phenomenon was made by Compton, the effect is now
known as the Compton's Effect.
Definition
The phenomenon in which a photon (hv) strike with stationary
electron and after collision both scattered in different direction in
such a way v > v is known as Compton Effect.
Consideration
In order to explain this phenomenon we assume that photon strike with a
stationary electron and after collision both makes an angle θ and ф
with respect to their initial line of motion.
Write note on Pair Production and Annihilation of Matter.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
PAIR PRODUCTION
Definition
The phenomenon in which photon collides with heavy nucleus then two
material particles, electron and positron are produced, is called Pair
Production.
Explanation
The positron produced during pair production has been identified to be
identical with an electron in mass and carries an equal positive charge
and is called the anti particle of electron. Since the process of pair
production involves the creation of particle and its anti particle,
therefore it is also known as materialization of energy. This
phenomenon is the practical proof of Einstein's mass energy equivalence,
in which mass and energy of the system remains constant.
For the production of electron and positron 1.02 MeV energy is required. I can be calculated by the following equation
Eo = 2moC(2)
=> Eo = 2 x 9.1 x 10(-33) x (3 x 10(8))2 / 1.6 x 10(-19)
=> Eo = 1.02 x 10(6) cV
=> Eo = 1.02 MeV
If energy of photon is less than 1.02 MeV then this phenomenon cannot
produce. If energy of photon is greater than 1.02 MeV then rest of
energy is used to accelerate the electron and Positron. The energy
conservation in Pair Production demands.
hv = e+ + e + K.E + K.E+
=> hv = moc² + moc² + K.E + K.E+
=> hv = moc² + K.E + K.E+
ANNIHILATION
Definition
The phenomenon in which electron and positron fuse together to form at least two photons, is known as Annihilation of matter.
Explanation
Annihilation is the reverse process of pair production. In Pair
Annihilation a particle and one of its anti particle come close enough
to be converted completely into radiation energy of the two photons
moving in opposite direction conserving the total momentum of the
creation and annihilation process. Each photon will have an energy equal
to rest mass energy moc of an electron that is equal to 0.51 MeV.
The energy conservation equation for the process will be
(mo)e + c² + K.Ee + (mo)e-c² + (K.E_e = 2hv
Conclusion
The phenomenon of Pair Production and annihilation helps us to conclude that energy and mass are inter changeable.
Write note on Uncertainty Principle
UNCERTAINTY PRINCIPLE
Introduction
In classical physics we can easily determine the momentum and position
of moving body simultaneously with accuracy, that no uncertainties are
involved in it. But for a light particle is found that however refined
we make our instruments there is a fundamental limitation to the
accuracy with which the positron and momentum can be known
simultaneously.
This limitation was first expressed by Hersenberg in 1927 and is known as Uncertainty Principle.
Statement
It is impossible to measure with accuracy both positron and momentum of a particle simultaneously.
Consideration
Consider a slit of thickness Δy placed near to a screen. Now a particle
bean strikes the slit then after diffraction at very small angle, it
reaches at points A.
Proof
As we know that momentum is a vector quantity, therefore, it can be resolved into two components. Consider ΔOAB.
tan θ = Perpendicular / Base
=> tan θ P(y) / P(x)
Since θ is very small, therefore
tan θ ≈ θ
=> θ P(y) / P(x)
=> Py = Px θ ------- (I)
From the condition of interference,
mλ = d sin θ
For first maximum,
m = 1
=> λ = Δy sin θ
But,
sin θ ≈ θ
=> λ = Δy θ
=> θ = λ / Δy
Substituting the value of θ in eq (I)
=> P(y) = P(x) λ / Δy
=> P(y)Δy = P(x) λ
From Debroglie's wave equation
λ = h / P(x)
=> λP(y)Δy = P(x) h / P(x)
=> P(y)Δy = h
Similarly,
P(x)Δx = h
And,
P(z)Δz = h
Conclusion
The uncertainty principle is of no importance in our daily life because
plank's constant h is very small and so the uncertainties in position
and momentum of even light objects are far too small to be
experimentally observed.
State and explain Debroglie's Hypothesis.
DEBROGLIE'S HYPOTHESIS
Introduction
In 1924, Debroglie proposed an idea called Debroglie's Hypothesis.
Statement
If light can have particle behaviour then material particles such as
electrons and protons etc can also behave in a wave like manner.
Mathematical Form
According to Debroglie's Hypothesis a particle like electron can possesses a momentum given by
P = mv = h / λ
Where m is the mass of particle. This relation has related the electron
a particle and the wave character of a frequency. Thus we can write
down the wave length associated with the particle i.e.
λ = h / mv
Conclusion
The Debroglie's relation was initially developed for the electron but
it is valid for all material objects including particles. However for
massive materials the associated wavelength is too small to be
measured.
Define and Explain Photoelectric Effect
PHOTOELECTRIC EFFECT
Introduction
In 1887, Hertz discovered the phenomenon of emission of electrons. When
ultra violet light falls on certain metals. On the basis of his
experimental results, he proposed the phenomenon of photoelectric
effect.
Definition
The emission of electrons from a solid or liquid surface when it is
subjected to electromagnetic radiation is known as Photo-electric
effect.
Experiment
Consider a glass tube in which two electrodes are suspended connected
to a positive and negative terminal of a battery. A milliammeter is
connected in series with the circuit to detect the flow of current.
When ultra violet rays strike the negative plate, then electrons emit.
These electrons are repelled by the negative (-) plate and attracted by
the positive plate. Hence, current flows in the circuit. The effect is
known as Photoelectric effect.
Maximum K.E of Electrons
The maximum K.E. of electrons can be achieved by reversing the polarity
of the circuit. When ultra violet rays strike the positive (+)
electrode. The kinetic energy possessed by the electrons can be achieved
if it is balanced by the voltage. So we increase the voltage to such
an extent that no electrons emit out. At this stage K.E. is maximum and
can be calculated by
K.E(MAX) = Voe
=> 1/2 mv² = Voe
Where,
m = mass of electron
e = charge of electron
v = velocity of electron
Vo = voltage of circuit
Results Obtained
The conclusions that were made from the experiment on Photoelectric effect are
1. Increasing the intensity of source of light increases the number of
photoelectrons but not the velocity with which it leaves the metallic
surface.
2. For each substance, there is a certain frequency called the threshold frequency below which the effect does not occur.
3. The higher the frequency of incident ray, the greater the K.E of electrons.
Photoelectric effect could not be explained on the basis of classical wave theory, because according to the theory:
- There should be no threshold frequency because by that time
electrons might escape from the metallic surface by absorbing enough
energy.
- The velocity of photelectrons should depend upon the intensity of the incident ray rather than the frequency.
Give Einstein's explanation of the photoelectrons effect on the basis of quantum theory of radiation.
EINSTEIN'S EXPLANATION OF PHOTOELECTRONS EFFECT
Introduction
Albert Einstein was successful in providing an explanation of the
photoelectric effect. He proposed his description on the basis of
quantum theory of radiation.
Explanation
Einstein explained the photoelectric effect on the basis of following postulates.
1. An electron absorbs neither one whole photon or it absorbs none.
2. An electron cannot absorb more than one photon.
3. After absorbing a photon, it acquires energy (hv) equal to photon.
The energy is either used up in ejecting the electrons or it dissipates
within the metal surface.
4. An electron may lose some of its energy before leaving the metal surface and is ejected with a kinetic energy less than hv.
5. If the energy of the photon is less than the energy required to overcome the forces then the electron will not emit.
Mathematical Expression
The energy of the electron is given as
Total Energy = Work Function + K.E
=> hv = фo + 1/2 mv²
фo = hvo
=> hv = hvo + 1/2 mv²
=> hv - hvo = 1/2 mv²
=> h(v-vo) = 1/2 mv²
Since, K.E = 1/2 mv² = Voe and v = c/λ
=> h [c/λ - c/λo] = Voc
=> hc [1/λ - 1/λ] = Voc
The above equation is known as Einstein's Photoelectric Equation.
What is a Photo Cell? Also Write its Uses.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
PHOTO CELL
Construction
The Photocell or photo tube consist of an evacuated glass tube fitted
with an anode and a concave metallic cathode of an appropriate surface.
The material of the cathode can be choosen to respond to the frequency range over which the photocell operates.
Working
When light of suitable frequency fall on the cathode photoelectrons are
emitted which are attracted by the positive anode and current flows in
the external circuit. The current would cease to flow if the light
beam is interrupted.
USES OF PHOTO CELL
1. Simple Photo Cell
A simple photo cell can be used in any situation where beam of light
falling on a cell is interrupted or broken. Examples are given below.
- To count vehicles passing a road or items running on a conveyer belt.
- To open door automatically.
- To operate burglar alarm etc.
2. Photo Conducting Cell
In this cell internal photoelectric effect liberates free charge
carrier in a material and its electrical conductivity increases as much
as 10,000 times, Its uses are
- For detection and measurement of infrared radiations where the wavelength is of the order of 10(-6) m.
- As relays for switching on artificial lighting, such as streetlights.
3. Photo Voltaic Cell
Such cells are used as exposure meters to set the aperture of the camera.
4. Other Uses
Photocells are used for the production of pictures in television
cameras and the sound tracks on motion pictures. The sound information
is stored on the film in the form
Statement
Radiant energy comes out in discreat amounts or guanta of energy.
The energy E content of each quantum was directly proportional to the
frequency v.
Mathematical Form
E ∞ v
=> E = hv -------- (I)
Where h = Plank's constant = 6.63 x 10(-34) Js. Since,
c = vλ
=> v = c / λ
Thus equation (I) becomes
E = hc / λ
Where,
c = velocity of light = 3 x 10(8) m/s.
λ = wavelength of radiation
The energy of 'n' photons is given by
E = nλy
Where,
n = 0, 1, 2, 3 ......
electrons might escape from the metallic surface by absorbing enough
energy.
Advent of modern physics 2nd Year Physics Notes karachiboardnotes.blogspot.com ADVENT OF MODERN PHYSICS What are the basic postulates o...
May 17, 2014
Posted by Karachi Board Notes
The atomic spectra
2nd Year Physics Notes
karachiboardnotes.blogspot.com
THE ATOMIC SPECTRA
What are the basic postulates of Bohr's Atomic Thoery?
Introduction
Neil Bohr studied the spectrum of hydrogen atom. On the basis of his
study, he proposed a theory, which is known as Bohr's Atomic theory.
POSTULATES OF BOHR'S ATOMIC THEORY
The important Postulates of Bohr's Atomic Theory are as follows:
Angular Momentum
Electrons revolve only in those orbits for which its orbital angular momentum is an integral multiple of h/2π, i.e.
L = mvr(n) = nh / 2π
Where,
m = mass of electron
V = velocity of electron
r(n) = radius of nth orbit
n = Principal quantum number
h = Plank's Constant
1. Energy
The total energy of an electron remains constant as long as it remains
in the same orbit. i.e. it does not radiate energy while revolving
around the nucleus.
2. Energy Release
When an electron jumps from a higher orbit having energy 'En' to a
lower orbit having energy 'Ep' then energy is released in the form of
energy 'hv' i.e.
Eo - Ep = hv = hc / λ
Where,
v = Frequency of Photon
λ = Wavelength of Photon
c = Speed of light
h = Plank's constant
Find out the radius, energy and wave number of hydrogen atom with the help of Bohr's Atomic theory.
HYDROGEN ATOM
A hydrogen atom is the simplest of all atoms. It consist of a proton
in the nucleus and an electron revolving around the nucleus.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
RADIUS OF HYDROGEN ORBIT
Consider an electron of charge '-e' revolving in a hydrogen atom around a proton of charge '+e' with constant speed v.
When the electron revolves around the nucleus, then two forces balance its motion.
Coulomb's Force = F = ke² / r² -------- (I)
Centrifugal Force = F = mv² / r ------- (II)
Comparing eq (I) and (II)
ke² / r² = mv² / r
=> ke² / mv² = r² / r
=> r = ke² / mv² -------- (III)
According to Bohr's theory, angular momentum is an integral multiple of h/2π
mvr = nh / 2π
=> v = nh / 2π mr
=> 1/v = 2π mr / nh
Taking square of both sides
=> 1/v² = 4π² m² r² / n²h²
Substituting the above value in eq (III)
r = Ke² / m = 4π² m² r² / n²h²
=> r / r² = 4π² m k e² / n²h²
=> 1 / r = 4π² m k e² / n²h²
=> r = n²h² / 4π²m k e²
We know that,
k = 1 /4π Єo => 1 / k = 4π Єo
=> r = n²h² / 4 π² m e² x 4π Єo
=> r = n²h² Єo / π e²
The above equation gives the radius of hydrogen atom.
Radii of Various Orbits
Radius of first orbit of hydrogen atom is calculated by substituting the following values in the equation of radius.
n = 1
h = 6.25 x 10(-34) J.sec
m = 9.1 x 10(-31) kg
k = 9 x 10(9) Nm²/col²
e = 1.6 x 10(-19) col
r = (1)² (6.625 x 10(-34)² / 4² (9.1 x 10(-31) (9 x 10(9)) (1.6 x 10-19)²
=> r = 0.53 x 10(-10)m
=> r1 = 0.53 Aº
For other orbits radius is given by
r2 = (2)² x 0.53 Aº
r3 = (3)² x 0.53 Aº
Similarly,
rn = n² x 0.53 Aº
ENERGY OF HYDROGEN ELECTRON
An electron revolving in the orbit of hydrogen atom possesses kinetic
energy as well as Potential Energy. Therefore, total energy is given by
E = K.E + P.E ------ (I)
Kinetic Energy
When an electron revolves in the orbit, then coulomb's force is balanced by centrifugal force
ke²/r² = mv²/r
=> mv² = ke²/r
=> 1/2 mv² = ke²/2r
=> K.E = ke²/2r
Potential Energy
Potential energy is given by
P.E = F.dr
=> P.E = Ke² / r² dr
=> P.E = ke² 1 / r² dr
=> P.E = ke² |-1/r|
=> P.E = -ke² [1/r - 1/∞]
=> P.E = -ke² (1/r - 0)
=> P.E = -ke² / r
Total Energy
Substituting the values of K.E and P.E in eq (I)
E = ke² / 2 - ke² / r
=> E = k2² / 2r
Since,
r = n² h²/ 4π² m k e²
=> E = ke² / 2 4π² m k e² / n² h²
=> |E = 2π² m k² e² / n² h²|
The above equation gives the energy of the orbits of hydrogen atom.
Negative sign shows that the electron is bound with the nucleus. When
energy of the electron becomes positive, then electron will leave the
nucleus.
WAVE NUMBER
When art electron jumps from higher orbit to inner orbit, then it radiates energy in the form of photons.
Explain the spectrum of hydrogen atom.
SPECTRUM OF HYDROGEN ATOM
When an electron jumps from a higher orbit to a lower orbit, it
radiates energy which appears in the form of a spectral line. A set of
such spectral lines is known as hydrogen spectrum. Hydrogen spectrum is
the simplest one which consists of five series.
1. Layman Series
When an electron jumps from a higher orbit to the first orbit, Laymen Series (ultra violet region) is obtained.
The wavelength and wave number of Laymen Series can be calculated by
v = R(H) (1/1² - 1/n²)
Where n = 2, 3, 4, ......
2. Balmer Series
When an electron jumps from a higher orbit to the second orbit then Balmer Series (visible region) is obtained.
The wavelength and wave number of Balmer Series can be calculated by
v = R(H) (1/2² - 1/n²)
Where n = 3, 4, 5, ......
3. Paschen Series
When an electron jumps from a higher orbit to the third orbit then Paschen Series (infra red region) is obtained.
The wavelength and wave number of Paschen Series can be calculated by
v = R(H) (1/3² - 1/n²)
Where n = 4, 5, 6, ......
4. Bracket Series
When an electron jumps from a higher orbit to the fourth orbit then Bracket Series (infra red region) is obtained.
The wavelength and wave number of Bracket Series can be calculated by
v = R(H) (1/4² - 1/n²)
Where n = 5, 6, 7, ......
5. Pfund Series
When an electron jumps from a higher orbit to the fifth orbit then Pfund Series (infra red region) is obtained.
The wavelength and wave number of Pfund Series can be calculated by
v = R(H) (1/5² - 1/n²)
Where n = 6, 7, .....
Write a note on spectra of X-rays. Also write down the properties.
Introduction
X-Rays were discovered by W.K. Roentgen are also known as Roentgen
rays. These rays of shorter wavelength, ranging from 0.1 nm to i nm.
X-rays are produced if heavier atoms are bombarded by energetic
electrons.
PRODUCTION OF X-RAYS
A Filament F and target T are produced in a vacuum chamber and voltage
V is applied across the ends. Electrons are produced by heating the
filament. These electrons are accelerated towards the metal by applying
very high voltage (several thousands volts). When electrons hit the
target, then X-rays are produced. There are two types of spectra
obtained from this experiment.
1. A continuous spectrum of frequencies or X-rays Brems Strahlung.
2. Characteristics spectrum or a line spectrum of a limited number of fairly definite frequencies.
1. Continuous Spectra
When electrons hit the metal target, a continuous spectrum of
frequencies of X-rays is emitted. The frequencies depend upon the
accelerating voltage and are very nearly independent of the material of
target.
Continuous spectrum is produced when electrons pass close to the atomic
nuclei. The are deflected and slowed down due to which they lose their
energy. The energy lost by decelerating electrons appears in the form
of photon in the X-ray range. The process is represented as
Atoms + e(Fast) -----> Atom + e(Slow) + hv
2. Characteristic Spectra
In the heavy atoms, electrons are assumed to be arranged in concentric
shells at increasing distance from the nucleus. The electrons of inner
shell are much tightly bound as compared to the electrons of outer
shells. Therefore, a large amount of energy is required to displace
them Consequently photons of larger energy are emitted when atoms are
stabilized. Thus the transition of inner shell electrons gives rise to
high-energy spectra or Characteristic spectra. To obtain characteristic
spectra, target metal of higher atomic number is used.
The process of emission of characteristic spectra takes place as
follows. When a highly energetic incident electrons knocks an electron
from the k-shell, a vacancy occurs in that shell. This vacancy is filled
by the arrival of an electron from outside the k-shell, emitting
excess amount of energy in the form of photon.
If the electrons jumps only one shell and returns with the emission of
X-rays to Y shell, then X-rays are termed as 'Yα' X-rays. If the
electron jumps two shells and returns with emission of X-rays to
suppose 'Y' shell, then X-rays are termed as 'Yβ' rays and so on, where Y
may be K, L, M, ......
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
PROPERTIES OF X-RAYS
1. X-rays are highly energetic radiation.
2. X-rays are the most shortest radiations.
3. X-rays are electromagnetic radiations that move with the speed of light.
4. X-rays have high penetrating power.
5. X-rays move in straight line and produce shadow when an obstacle is placed in front of them.
6. X-rays are not deflected by electric and magnetic fields.
7. X-rays produce ionization in gases and eject electrons from certain metals.
8. X-rays produce fluorescence in many substances.
9. X-rays being electromagnetic waves can be reflected, refracted, diffracted and polarized under suitable conditions.
USES OF X-RAYS
1. The major use of X-rays is in medical and diagnostic treatment.
2. X-rays are used at customs and security posts.
3. The diffraction property of X-rays is used to detect arms, explosives
The atomic spectra 2nd Year Physics Notes karachiboardnotes.blogspot.com THE ATOMIC SPECTRA What are the basic postulates of Bohr's...
May 17, 2014
Posted by Karachi Board Notes
The atomic nucleus
2nd Year Physics Notes
karachiboardnotes.blogspot.com
THE ATOMIC NUCLEUS
NUCLEAR STRUCTURE
The nucleus consists of protons and neutrons. A protonis a positively
charged particle having mass 1.6726 x 10(-27) kg and charge 1.6 x
10(-19) coulomb. The charge of the proton is equal in magnitude of the
charge of an electron, but opposite to it in sign. Neutrons have no
charge. Its mass is 1.6750 x 10(-31). The mass of proton is 1836 times
the mass of an electron.
MASS NUMBER
The sum of the number of protons and neutrons in a nucleus is called Mass Number.
It is denoted by 'A'. This number is also called Nucleus Number.
ATOMIC NUMBER
The number of protons in a nucleus is called Atomic Number or proton number or charge number.
It is denoted by 'Z'.
NEUTRON NUMBER
The difference between mass number and atomic number is called Neutron Number.
It is denoted by 'N' and is given by
N = A - Z
REPRESENTATION OF AN ELEMENT
An element X having mass number A and atomic number Z is represented by the symbol zXA.
Where X is the chemical abbreviation for the particular element.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
ISOTOPES
The elements having same atomic number but different mass number or neutrons number are called isotopes.
For example hydrogen deuterium and tritium
Hydrogen A = 1, Z = 1, N = 0
Deuterium A = 2, Z = 1, N = 1
Tritium A = 3, Z = 1, N = 2
Explain the phenomenon of radioactivity.
Introduction
Henri Bacqural discovered that Uranium atoms (z = 92) emit highly
penetrating radiations that could penetrate paper, glass and even
aluminium. On the basis of his experimental results, he explained the
phenomenon of radiation.
Definition
The phenomenon of spontaneous disintegration of nucleus of atoms is known as radioactivity.
Explanation
Radioactivity is a self-disrupting activity exhibited by some naturally
occurring elements. It has been found, that the elements with atomic
number greater than 83 are unstable and emit certain type of
radiations. Such substances (e.g. Uranium, Radium, Thorium) are called
Radio-active substances and the radiations emitted from their nuclei are
called radio active radiations and the phenomenon is known as
Radioactivity. Rutherford and his co-workers proved that the radiations
emitted by a radio active substance are of three different types.
Experiment
Radio Active radiations can be separated by applying electric or
magnetic field to the element. A small amount of radioactive substance
is placed at the bottom of a cavity drilled in a block of lead. When the
narrow beam of radioactive rays is allowed to pass through the space
between the two charged plates, the path of some rays bend. A similar
effect is observed in the presence of magnetic field.
Results Obtained
The conclusion that were made fro the experiment are
1. α - Particles
The rays towards the negative plate indicate that they consist of positively charged particles. These were named as α-rays.
2. β - Particles
The rays bending towards the positive plate indicate that they consist
of negatively charged particles. These were named as β (beta) rays.
3. γ - Rays
The rays that go undeflected indicate no charge and are therefore energetic photons or γ (gamma) rays.
Properties of α - Particles
1. α - Particles are Helium nuclei. The charge of a α-particle is twice
the charge of a proton and its mass is four times than that of
a-proton.
2. The speed of α-particles is 1/100 times the speed of light.
3. They produce fluorescence and effect the photographic plate.
4. α - Particles have low penetrating power.
5. They have high ionization power.
6. When a nucleus zXA disintegrates by the emission of an α-particles,
its charge number (z) decreases by 2 and mass number (A) decreases by
4.
zXA ----> Z2 (VA.4) + α - Particle
Properties of β - Particles
1. β - Particles are electrons with more energy as compared to ordinary
electrons because their origin is nucleus and not the atomic orbits.
2. The speed of β - particles is 1/10 times the speed of light.
3. They produce fluorescence and affect the photographic plate.
4. β - particles have greater penetrating power then α-particles.
5. They have low ionizing power.
6. When a nucleus zXA disintegrates by the emission of β - particle,
its charge number (Z) decreases or increases by 1, while mass number
remains same.
zXA ----> z+1 γA + -1βº (electron)
zXA ----> z-1 γA + +1βº (positron)
Properties of γ - Rays
1. γ - Rays are energetic photons and have no charge. They are similar to X - rays but more energetic.
2. They travel with the speed of light.
3. The produce fluorescence and affect the photographic plate.
4. Their penetrating power is very high.
5. They do not have any ionization power.
6. When γ - Rays emit out from the nucleus of a radio active substance,
then the mass number (A) and charge number (Z) remain same
zXA ----> zXA + γ - Rays
Where zXA represents the nucleus in excited state.
Define and explain the law of radioactive decay. How can you
determine the half life of a radioactive substance with the help of this
law?
Statement
The rate of decay in a radioactive process is directly proportional
to the number of parent nuclides, present in the unstable nuclides of
the given species.
Mathematical Form
If ΔN be the number of nuclides disintegrated in time Δt and N be the number of Nuclides at time t, then:
ΔN ∞ N
ΔN ∞ Δt
=> ΔN ∞ NΔt
=> ΔN = -λNΔt
=> ΔN / Δt = -λN
Where is the decay constant and negative sign shows that number of atoms decrease w.r.t
=> 1/N ΔN = - λΔt
=> ΔN / N= - λΔt
HALF LIFE OF ELEMENT
Definition
It is the time in which half of radioactive elements decays from paront element to daughter element.
It is denoted by T 1/2.
Example
Suppose we have 10,000 radioactive atoms. If in 10 seconds, 50,000 of
them decay, then this time is called the half life that radioactivity
element.
Explain nuclear fission reaction also discuss its type.
Introduction
In 1943, Fermi, Serge and their co-workers studied the phenomenon of
nuclear studies the phenomenon of nuclear reactions. On the basis of
their experimental results they proposed a remarkable reaction. This
was advanced by many scientist and fission reaction was discovered.
Definition
The process in which a heavy nucleus breaks up into two lighter
nuclei of nearly equal masses after bombardment by a slow neutron is
known as nuclear fission.
Explanation
When an isotope of uranium of 92U235 is bombarded with slow moving
neutrons, then fission reactions takes place. During this process two
new elements three neutrons and a large amount of energy is released.
The two nuclei of new elements produced are Barium and Krypton. The
nuclear fission reaction.
Barium and Krypton are known as Fission pigments, which are radio
active. A large amount of heat energy is also liberated, which may be
produced.
CHAIN REACTION
Fission reaction is a chain reaction that has been classified into the following two types.
1. Controlled Fission Chain Reaction.
2. Uncontrolled Fission Chain Reaction.
1. Controlled Fission Chain Reaction
In a fission reaction for one atom of uranium, three neutrons are
produced, which may give rise to fission reaction in other uranium
atoms. If two neutrons out of three are stopped then chain reaction
takes place at uniform rate and a fixed amount of energy is obtained.
This is done by usually Cadmium or graphite rods. In a nuclear reactor
controlled chain reaction takes place.
2. Uncontrolled Fission Chain Reaction
If in a fission reaction, the number of neutrons is not controlled,
then the reaction will build up at a very fast rate and in only few
seconds, an explosion occurs. In an atom bomb, uncontrolled fission
chain reaction takes place.
@import "/extensions/GoogleAdSense/GoogleAdSense.css";
Define and explain the phenomena of Nuclear Fusion.
NUCLEAR FISSION
Definition
A process in which two light nuclei combine (or fuse together) to
form a heavy nucleus and energy is released is called Nuclear Fusion.
The energy released is called Thermo-Nucleus Fusion Energy.
Explanation
For example when light nuclei of hydrogen are combined to form a
heavier nucleus of helium energy is liberated. The final mass is smaller
than the initial mass and the deficit of mass is comparatively greater
than in fission. For this reason the energy liberated in the process
of fission.
It is very difficult to produce fusion reaction due to the fact that
when two positively charged nuclei are bought closer and closer and
then fused together. Work has to be done against the electrostatic
force of repulsion. This requires a great deal of energy.
Fusion reaction can produce great amount of energy. The raw material 1
the reaction is deuteron, which is found in abundance in world oceans
as heavy water.
The fusion reaction is possible in sun and stars because of very high
temperature. The fusion reactions are also the basic source of energy
in stars including the sun.
This process is called Proton-Proton cycle. In this fusion process the amount of energy released is of the order of 25 MeV.
Another fusion process is suggested by Bethe. It is called
Carbon-Nitrogen cycle or simply Carbon Cycle. This process is assumed to
occurs in the sun. In this process four protons are converted into an
alpha particle with carbon acting as a catalyst in the reaction
The atomic nucleus 2nd Year Physics Notes karachiboardnotes.blogspot.com THE ATOMIC NUCLEUS NUCLEAR STRUCTURE The nucleus consists of ...