To The Richardson-dushman Equation And To Find Out The Work Function Of The Electron Emitting Material. 4l1u29

Serial Number

Topic

Page Number

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Aim

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Apparatus

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Theory

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Procedure

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Observation Table

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Calculations

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Graph

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Percentage Error

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Result

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Precautions

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Bibliography

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Member List

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AIM To the RichardsonDushman equation and to find out the work function of the electron emitting material.

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APPARATUS     



Standard Resistance Decade Resistance Box Galvanometer Micro- Ammeter Power Supply Rheostat 4

APPARATUS

5

CIRCUIT DIAGRAM

6

THEORY WORK FUNCTION In solid state physics, the work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is a characteristic property for any solid face of a substance with a conduction band (whether empty or partly filled). For a metal, the Fermi level is inside the conduction band, indicating that the band is partly filled. For an insulator, the Fermi level lies within the band gap, indicating an empty conduction band; in this case, the minimum energy to remove an electron is about the sum of half the band gap and the work function. 7

Work Function of various elements

ELEMENT

ev

ELEMENT

ev

ELEMENT

ev

ELEMENT

ev

ELEMENT

ev

Ag:

4.52-4.74

Al:

4.06-4.26

As:

3.75

Au:

5.1-5.47

B:

~4.45

Ba:

2.52-2.7

Be:

4.98

Bi:

4.34

C:

~5

Ca:

2.87

Cd:

4.08

Ce:

2.9

Co:

5

Cr:

4.5

Cs:

2.14

Cu:

4.53-5.10

Eu:

2.5

Fe:

4.67-4.81

Ga:

4.32

Gd:

2.90

Hf:

3.9

Hg:

4.475

In:

4.09

Ir:

5.00-5.67

K:

2.29

La:

4

Li:

2.93

Lu:

~3.3

Mg:

3.66

Mn:

4.1

Mo:

4.36-4.95

Na:

2.36

Nb:

3.95-4.87

Nd:

3.2

Ni:

5.04-5.35

Os:

5.93

Pb:

4.25

Pd:

5.22-5.6

Pt:

5.12-5.93

Rb:

2.261

Re:

4.72

Rh:

4.98

Ru:

4.71

Sb:

4.55-4.7

Sc:

3.5

Si:

4.60-4.85

Sm:

2.7

Sn:

4.42

Sr:

~2.59

Se:

5.9

Ta:

4.00-4.80

Tb:

3.00

Te:

4.95

Th:

3.4

Ti:

4.33

Tl:

~3.84

U:

3.63-3.90

V:

4.3

W:

4.32-5.22

Y:

3.1

Yb:

2.60

Zn:

3.63-4.9

Zr:

4.05

PHOTOELECTRIC WORK FUNCTION The work function is the minimum energy that must be given to an electron to liberate it from the surface of a particular substance. In the photoelectric effect, electron excitation is achieved by absorption of a photon. If the photon's energy is greater than the substance's work function, photoelectric emission occurs and the electron is liberated from the surface. (Excess photon energy results in a liberated electron with non-zero kinetic energy.) The photoelectric work function is φ=h f˳ where h is Planck's constant and f˳ is the minimum (threshold) frequency of the photon required to produce photoelectric emission

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THERMOINIC EMISSION Thermionic emission is the heat-induced flow of charge carriers from a surface or over a potential-energy barrier. This occurs because the thermal energy given to the carrier overcomes the forces restraining it. The charge carriers can be electrons or ions, and in older literature are sometimes referred to as "thermions". After emission, a charge will initially be left behind in the emitting region that is equal in magnitude and opposite in sign to the total charge emitted. But if the emitter is connected to a battery, then this charge left behind will be neutralized by charge supplied by the battery, as the emitted charge carriers move away from the emitter, and finally the emitter will be in the same state as it was before emission. The thermionic emission of electrons is also known as thermal electron emission.

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RICHARDSON - DUSHMAN EQUATION The Richardson-Dushman equation relates the current density of a thermionic emission to the work function (W) and temperature (T) of the emitting material: J = A T2 exp(-W/kT) where, J is the current density of the emission (mA/mm2) A is Richardson's constant. A = 4*πmek2/h3 ~ 1202 mA/mm2K2, where m is the mass of electron, e is elementary charge, and h is Plank's constant. In practice, A may be multiplied by a correction factor that depends on the material (see Table I below). Note that A varies from about 32 to 160 A cm-2 K-2 for pure (polycrystalline) metals and over a much greater range for oxide and composite surfaces. T is temperature (K) W is the work function of the cathode material (J)

k is the Boltzmann constant (1.38066E-23 J/K) 11

PROCEDURE 1. Connect the circuit as shown in the figure. 2. Once connections are made keep plate voltage at about 100V.

3. Raise filament current by decreasing RH slowly till filament is just glowing. It is better to enclose the valve in a dark chamber to observe just glowing condition. Wait for a few minutes to observe the steady state condition. 4. Adjust R2 (do not make it less than 50 ohm) to obtain balance. Note R1, R2, R. 5. Again decrease RH (that is increase filament current) so that galvanometer shows some deflection of the centre. Wait for a few minutes to obtain steady condition. Changing R2 obtain balance and note R2. 6. Without disturbing bridge circuit raise high tension and observe milli - ammeter current I and keep on raising high tension till I becomes nearly constant. This is saturation current value. 12

OBSERVATION TABLE Least Count of milliammmeter=0.1 mA R=1Ω R1=10Ω R2=90Ω(at just glowing condition) Serial No.

R2

RT

(Ω)

I (mA)

1

95

0.1

9.5

2

106

0.2

2

109

3

T0

1/T0

1/T0²

i/T0²

(K)

(Kˉ¹)

(Kˉ²)

(mAKˉ²)

4.1

813

0.00123

1.5129E-06

1.5129E-07

6.74

10.6

4.6

905

0.001105

1.22103E-06

2.44205E-07

6.61

0.3

10.9

4.7

916

0.001092

1.19246E-06

3.57739E-07

6.51

117

0.6

11.7

5.1

976

0.001025

1.05063E-06

6.30375E-07

6.31

4

123

0.9

12.3

5.33

1027

0.000974

9.48676E-07

8.53808E-07

6.12

5

131

1.2

13.1

5.68

1106

0.000904

8.17216E-07

9.80659E-07

5.96

6

141

1.7

14.2

6.15

1160

0.000862

7.43044E-07

1.26317E-06

5.82

7

152

2.5

15.2

6.6

1218

0.000821

6.74041E-07

1.6851E-06

5.75

RT/R0

(Ω)

Log(i/T0²)

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CALCULATIONS RT = R2/R1*R6 RG = RT/10*3.9Ω RG = 9/3.9 = 2.3 Ω Slope = W/2.303k = (Log(i/T02²)- Log(i/T01²))

1/T01²- 1/T02² = (-6.74-(-5.75))*10 -8.21+12.3

4

=2.234*10

4

W = (Slope)*2.303k

= 7.099*10-19 = 4.44 eV

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GRAPH

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PERCENTAGE ERROR Actual value of Work Function= 4.5eV Calculated value of Work Function= 4.44eV Error= Actual value - Calculated value = 4.5 eV – 4.44 eV = 0.06 eV Percentage Error = (Error/ Actual value )*100 = (0.06/4.5)*100 = 1.3%

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RESULT Since the graph is a straight line Richardson Dushman Equation is verified. Work function of the electron emitting material is 4.44ev.

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PRECAUTIONS 1. Before applying the power ensure that  

H.T. control of the power should be set to zero. Resistance of the resistance box R1 should be greater than or equal to 10 ohms. Resistance of the decade resistance box R2 should be never less than 50 ohms. During the experiment it can be changed to obtain balance. However it should not be made zero in any case.

2. When the connections are over check again for polarities of the supply , voltmeter and ammeter. 3. To observe just glowing condition enclose the valve in dark chamber. 4. Readings should be taken only after current obtains steady state.

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BIBLIOGRAPHY 1. Electromechanical devices for energy conversion and control systems by Vincent Del Toro 2. www.wikipedia.com 3. www.physics.nad.ru 4. www.howthingswork.com 5. Analytical experimental physics by Harvey Brace Lemon, Michael Ference

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