Dtails of Experiments PH-491

Determination of Planck’s constant using photo-cell

Theory:

From Einstein’s photoelectric equation, we know

hυ = hυ0+ 1

2mv

2

= hυ0+eVs

= + eVs

Where, υ= Frequency of incident light

υ0 = Threshold frequency

h= Planck’s constant

m= Mass of electron

v= Velocity of electron

e= Charge of a electron

Vs= Stopping potential

= hυ0 =Work function

Now if we draw a graph (υ Vs Vs) then from this graph we can get a slope sV

. Therefore from

the equation we can write,

sVh e

.

Experimental Result:

Colour of filter Wavelength

(nm)

Frequency

(Hz)

Stopping Potential

(Volt)

Red

Yellow I

Yellow II

Green

Blue

Calculation:

Conclusion:

Precaution and discussion:

1) Since the cathode of the photo-tube is sensitive to light and so the photo-tube is not

allowed to direct light exposure. Care has been taken during the change of filters and the

light source is covered in doing so.

2) On completing the experiment the entire set up is fully covered to prevent unwanted light

exposure and dust.

3) If adequate measure be not taken, the photo-tube will persistently decrease with exposure

to light due to ageing.

4) In order to maintain the life-time of the photo-tube, the standard procedure is to use

moderate intensity source of light.

Determination of dielectric constant of a given sample

Theory:

The dielectric constant is the ratio of the capacitor using that material as the dielectric in a

capacitor to the capacitance using vacuum as dielectric. All ferromagnetic material has a

transition temperature called Curie temperature. As temperature T >Tc the crystal does not

exhibit ferro-electricity. But for T < Tc sometimes show the phase transition through the Curie

point. For a ferro-electric ceramic like Barium Titanium Oxide (BaTiO3) there is a distinct

advantage because of its Preovskite structure. Much caution can be substituted on both Barium

and Titanium side without drastically changing the oval structure.

Dielectric constant 0

C

C

Capacitance in vacuum ( 0C ) 0 A

t

Area of the capacitor = 62.18 mm2

Thickness of the dielectric material = 1.89 mm

Permittivity of free space 0 = 8.854 x 10-12

F/m

Observation:

Variation of dielectric constant with temperature

Temperature (oC) Capacitance (pF) Dielectric constant( )

Graph:

A graph may be drawn by plotting Temperature in the X-axis and the Dielectric constant on the

Y-axis.

Calculation:

Conclusion:

Precaution & discussion:

1. Adequate care has been to ensure the consistency of temperature in each measurement.

2. The dielectric constant variation is systematic and the variation is quite sharp near

transition point so sufficient number of data has been generated near the peak value of

dielectric constant .This has a better effect and least error incorporated for transition

temperature measurement.

3. Care has been taken not to make or break the circuit; this will damage the experimental

set up altogether.

Determination of Stefan’s constant using a vacuum tube diode type

Ez-81

Theory:

In this experiment we use commercially available vacuum diode Ez-81 which has a cylindrical

cathode made of nickel. Inside the cathode there is a tungsten heater filament. Cathode is heated by

passing electric current through the tungsten heater filament. The temperature of filament can be

determined by using known resistance temperature (R-T) relationship for tungsten,

1.2

300 300

TR T

R

Where,

TR is the resistance of tungsten filament at T K

300R is resistance at 300K

It is possible to estimate the value of the resistance of the tungsten wire within Ez-81 at room

temperature for a very small voltage range following an extrapolation to zero volts. On the other

hand power generated by the tungsten wire is voltage multiplied by current. Neglecting other

modes of heat dissipation this is equal to the power radiated by the wire. Through the plot we can

calculate the resistance of the tungsten wire.

From Stefan’s Law, We get nP E ST

log log( ) logP E S n T

‘ ’ is Stefan’s constant.

‘P’ is power radiated by filament.

‘E’ is emissivity of the cathode surface = 0.24

‘S’ is the surface area of the cathode = 2.24 x 10-4

m2

Observation:

Resistance –Temperature data:

300

TR

R

T

1 300

4 920

6 1300

8 1645

10 1990

I-V data of the filament wire:

Vf

volt

If

amp

P = VfIf

Watt

RT

ohm 0.6

TR

ohm

T

K

logP

Watt

logT

K

Graph:

1. A graph will be plotted with the supplied value of 300

TR

R vs T

2. A graph will be plotted between log P (along Y-axis) and log T (along X-axis).

Calculation:

Conclusion:

**Standard value of = 5.67 x 10-8

W m-2

K-4


1. All the potentiometers are drifted initially to the lowest position before the circuit is

switched on. The electric circuit is kept for 5-7 minutes in order to attain the equilibrium

condition.

2. Due to vacuum, the loss of heat from the valve wall is very small and hence we can

assume that this is an almost black body condition.

3. The steps of reading are generated in such a way the data points are uniformly interposed

within the graph for yielding a proper value.

4. Since the main gadget of the instrument is an electronic valve so to preserve its lifetime

careful manipulation is required.

Determination of Band gap of a given semiconductor by four probe

method

Theory:

The highest filled energy band which includes electrons shared in covalent bonds or transferred in

ionic bonds in a semiconductor is known as valence band. The energy band which includes free

electrons is called conduction band. The energy gap between the top of the valence band and

bottom of the conduction band is known as band gap.

Band gap of the semiconductor (Eg) = Ec - Ev

Ec = Energy of the conduction band

Ev = Energy of the valence band

The band gap of a semiconductor can be found out by the formula

Loge log2

g

e

EA

kT

‘ ’ is the resistivity of the semiconductor.

‘k’ is the Boltzmann constant(=1.38 x 10-23

j/k or 8.6 x 10-5

eV/deg).

‘T’ is the absolute temperature.

‘A’ is a constant.

The resistivity of the given semiconductor is given by

0

7 ( / )G W S

The correction factor 7

2( / ) log 2e

SG W S

W

Again 0 2

VS

I

Where,

‘V’ is the applied voltage.

‘I’ is the current.

‘W’ is the thickness of the crystal = 0.55mm

‘S’ is the distance between the probes = 2mm

Observation:

Current (I) =

Temp.

t0c

Voltage

(mv)

Temp.

T K

T-1

x 10-3

K-1

0

( cm )

( cm )

loge

When temp.

increases

When temp.

decreases

Avg.

Graph:

Plot a graph of loge (along Y-axis) vs T-1

x 10-3

(along X-axis). Slope will give the value of

log

1e

T

.

Calculation:

Conclusion:

** Standard value of Eg = 0.7eV (in case of Ge- semiconductor)


1. Current should be kept constant throughout the experiment.

2. The germanium crystal is very brittle; therefore only minimum pressure is required for

proper electrical contacts.

3. All the observation should be noted while the temperature is falling.

Determination of Lande g factor by using Electron spin resonance

spectrometer for a specimen DPPH

Theory:

Spin the intrinsic angular momentum, S, couples with the orbital angular momentum, L to give a

resultant angular momentum J. In present of external magnetic field, H0, 2J+1 magnetic sublevel

are created with equal energy difference.

0BE g H

Where, B is the Bohr magneton and g is a factor known as Lande g-factor, which is given by

1 1 11

2 1

J J S S L Lg

J J

1 2 3

6 5 4

RF Oscillator Detector AF Amplifier

Cathode Ray

Tube

Sweep Unit Phase Shifter

Ground

S

p

e

c

i

m

e

n

Helmholtz

Coil

Electron Spin Resonance Spectrometer

Now if the particle is subjected to a perturbation by an alternating magnetic field with frequency

1 such that the quantum 1h is exactly the same as E given in equation and if the direction of

the alternating field is perpendicular to the static magnetic field then there will be transition

between neighboring sublevels according to selection rule 1Jm . Therefore, at the resonance

0 1BE g H h

If ‘I’ is the current flowing through the Helmholtz coil with ‘n’ no of turns in each coil and radius

‘a’ then the peak to peak magnetic field is produced.

Magnetic field 32

2 210 125

nH I

a

, which produces ‘P’ division of deflection in the X-direction

of the CRO screen and if distance between the two absorption peaks is ‘2Q’ division on the same

screen then

0

QH H

P

So,

1 1

0

10 125

2 2 32B B

h h P ag

H QI n

=

k

QI

Where,

1 10 125

2 2 32B

h P ak

n

Planck constant (h) = 6.625 x 10-34

J-S

1 = 10 M Hz

a = 7.7 cm

n = 500

B = .927 x 10-20

C.G.S unit

Observation:

Graph:

Plot 1

I along X-axis and ‘Q’ along Y-axis. The value of IQ is estimated from the slope of the

graph.

Calculation:

Conclusion:

**g = 2 for free electron


1. Copious amounts of unpaired electrons are present in the DPPH specimen and hence, the

experiment is an ideal one.

2. When set of a particular frequency the pot is not disturbed during the measurement. This

may cause erratic behavior in data taking event.

3. BNC connection is checked before the start of the experiment otherwise the signal to

noise ratio may reduced the quality of the end data.

4. The graphical picture proves the linearity in the data evaluation and also proves the ideal

nature of unpaired electron under ESR.

Current(I)

mA

1

I

P 2Q Q

80

100

120

140

160

180

Determination of e/m by J.J. Thomson’s method

Theory:

If ‘l’ is the length of the deflecting plate and ‘v’ is the velocity of the electron in horizontal

direction as emerging from the gun then the vertical velocity of the electron after emerging from

the deflecting plate is

y

e V lv

m d v

Here ‘V’ is the deflecting voltage, ‘e’ is the charge of an electron and ‘m’ is the mass of the

electron. Separation between the deflecting plates is ‘d’.

After emerging from the deflecting plates if this electron traverses ‘L’ distance horizontally to

reach the screen then the vertical deflection is given by

e V l LD

m d v v

Where, l << L

If two bar magnets are placed on the east-west arm and can nullify the deflection produced by

the electric field then

Ve evB

d

Now we get

2

e V

m BlLd

D

If ‘ ’ is the deflection angle of the compass needle produced by the same magnetic field which

nullified the deflection of the electron beam then the magnetic field (B) = BH tan ,where, BH is

the horizontal component of earth’s magnetic field.

‘l’ = 1.5cm

‘L’ = 20cm

‘d’ = 2cm

BH = 0.38 x 10-4

tesla

Observation:

Applied voltage

Volt

D

m

B

T

2B

D

T2/m

Graph: A graph may be drawn by plotting 2B

D in the Y-axis and the voltage ‘V’ along X-axis.

Slope of the curve may be used in the working formula to estimatee

m.

Calculation:

Conclusion:

** e

m = 0.1758 x 10

12 c/kg

Precaution and discussion:

1) The axis of the cathode ray tube is adjusted to be strictly along the magnetic meridian.

2) The green spot on the screen is adjusted to minimum visible brightness level in order to

prevent the screen from burning.

3) The oscillation of the magnetic needle should be of small amplitude.

4) Care has been taken to check that low magnetic material is initiate vicinity of the

experiment set up.

5) The potentiometer control is always brought to minimum potential before switching on or

off the power supply.

6) It is imperative to keep the bar magnets inside the box by placing appropriate ke

Determination of Hall co efficient of a semiconductor

Theory:

We know the static magnetic field has no effect on the charges unless they are in motion. When

charges flow, a magnetic field directed perpendicular to the direction of flux produced a

mutually perpendicular force on the charges. When this happens, electrons and holes will be

separated by opposite forces. They will in turn produce an electric field (En) which depends on

the cross product of magnetic intensity (H) and the current density (J).

nE R J H

‘R’ is called Hall coefficient. Now we consider a bar semiconductor having dimension x, y and

z. Let J be directed along x and H along z, then En will be along y axis.

In general Hall voltage is not a linear function of applied magnetic field, that is the Hall

coefficient is not generally constant, but a function of the applied magnetic field.

The working formula is h

h

V tR

I H

‘I’ is current flowing through the semiconductor.

‘t’ is the thickness of the semiconductor.

‘Vh’ is Hall voltage.

t = 0.5 mm

Observation:

Calibration curve data table

Distance between the poles =

Hall current- Hall voltage data at constant magnetic field

Magnetic field = Gauss

Graph:

1. Draw a graph of Magnetizing current (along X axis) vs Magnetic field (along Y-axis).

2. Draw a graph hall current (along X axis) vs hall voltage (along Y axis). Determine the

slope.

Calculation:

Magnetizing current

amp

Magnetic field

Gauss

Magnetizing current Magnetic field (H) Hall current(Ih) Hall voltage(Vh)

Conclusion:


1) Hall probe connections are made in such a way and it is imperative not to touch or adjust

the connections, otherwise the entire experiment will become meaningless.

2) The sample is very brittle and hence careful handling is maintained.

3) The Hall probe is properly centered and oriented in the magnetic field such that

maximum Hall-voltage is generated

4) The initial Hall-voltage without magnetic field is continuously monitor throughout the

experiment and has been subtracted from the actual Hall-voltage reading.

5) The sample current is not exceeded beyond the prescribed stipulation.

6) The movable pole pieces of the electromagnet are symmetrically moved in order to avoid

asymmetric in the magnetic field.

7) Magnetic field is varied gradually in steps to avoid damage the electromagnetic coils.

Verification of Bohr’s atomic orbital theory through Frank-Hertz

experiment

Theory:

From Bohr’s postulation we know that the internal energies of an electron of an atom are

quantized. We can directly prove this postulation by this experiment.

In this experiment set up there is a tetrode tube filled with argon vapour. Electrons

emitted by heated filament are accelerated by the potential VG2K (applied between cathode and

grid 2). At first some electron reach to the plate A provided that their K.E. is sufficient to

overcome the retarding potential VG1K (applied between cathode and grid 1). So, initially we see

that the plate current increases with increase of VG2K. But as the voltage further increases, the

electron energy reaches to the threshold value to excite the atom in its first excited state, the

current abruptly drops. When the VG2K is increased further, again the current starts to increase

and when VG2K reaches to a value twice that of first excitation potential again we get the current

drops. This way, we get that the current drops 4-5 times at certain voltage range. This

observation proves that the energies of the atom are quantized.

A

Nanometer

G2

G1

K VG2K

VG2A

V G1K

Observation:

VG1K= 1.5 V, VG2A= 7.5 V

Plate current(I)

amp

VG2K

Volt

Measure the excitation potential from graph

Graph:

Draw a graph between I (along Y axis) and VG2K along (X-axis)

Calculation:

Conclusion:

Distance between the peaks

Volt

Average excitation potential

eV


1) The system is initially not on. All the pots are brought to zero (0) value. Then the system

is on.

2) Wait at least for 5 to 10 min. for maintaining equilibrium. The filament is fed with a

potential to commence emanation of carriers.

3) Wait for 2 to 3 minutes. Then plot the bias voltage as prescribed.

4) The switch is in zero position and the current scale is set at 10-7

position.

5) Care has been taken to change the VG2K with slow variation and wait at least 2 to 4 min.

for all measurements.

6) The bias voltage is changed by small range. Repeat the experiment for more

measurements.

7) Care has been maintained to switch off the apparatus by bringing all the pots to the zero

(0) values. And then turned off the switch. This is very important.

Dtails of Experiments PH-491

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Transcript of Dtails of Experiments PH-491