Electron And Photon

Electron and photon • The emission of electrons from the surface of the metal when light energy incident on it is called photo electric effect. • This effect was first discovered by Heinrich Hertz. • The emitted electrons in this process are called photoelectrons • The minimum energy required to emit the electron from metal surface is called as photo electric

work function

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Characteristics of Photo Electric Effect: • To produce photoelectric effect, the frequency of incident radiation must be greater than certain minimum frequency called as threshold frequency (v0).

• The wavelength corresponding to threshold frequency is called as threshold wave length (λ0). • Threshold wavelength is the maximum wavelength of incident light above which photoelectric effect does not observed. Safe Hands

Experiment conducted to study characteristics of photoelectron

V

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Lenard’s laws of photoelectric emission • The K.E. of emitted electrons in the effect is directly proportional to frequency of incident radiations, provided v > v0.

KE

Frequency ‘ν’ Safe Hands

Philipp Lenard

• Number of electrons emitted (means current) in this process is directly proportional to intensity of incident radiations

Current

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Intensity of light

• Photoelectric work function is different for different materials and same for one material. The minimum value of potential required to stop the emitted photo electrons is called as stopping potential (Vs). KEmax I2 I1

Vo Safe Hands

• Stopping potential is directly proportional to frequency of incident radiations.

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Outcomes of Lenard’s experiment and problems with classical mechanics • Photoelectrons are emitted only when the frequency of incident light is more than threshold frequency.According to Classical Theory it must be at all frequencies. • KEmax is independent of intensity of incident light.This was unexpected • The electron is given out in less than 10 –8sec. A time gap was expected Safe Hands

Einstein’s explanation • Einstein used Plank’s quantum theory to explain characteristics of photoelectric effect. • For this work Einstein awarded a Nobel Prize in 1921 • According to Einstein, the theory of photon incident on metal surface is utilized for two purposes – (1) to remove the electron from the metal surface and – (2) to provide K.E. to emitted electrons. Safe Hands

2 hν = W + ½ mv • o max 2 hν = hν + ½ mv • o max

• KEmax = h(ν- νo) • When intensity of light increases the energy of photon (hν) remain same but number of photon increases thereby increasing the current. Safe Hands

• This simple equation explains everything— • KEmax = hν - hν0 represents line with slope h and –ve Y- intercept ( recall y = mx + c ) called as work function • Photoelectric work function is same as thermionic work function • If ν - ν0< 0 then there will be no emission as KEmax will be –ve. • Using relation c = λν, KEmax = hc/λ - hc/λ0 hence Kemax = hc(1/λSafe-Hands 1/λ0)

Some points to be known

• Photoelectric effect was discovered by Hertz – studied by Lenard – explained by Einstein using plank’s theory and shown by most of metals for UV and alkali metals show this effects for visible also this was found by Elster and Geital. • Photocells are of three types Photo emissive, photovoltaic and photoconductive. • Use of photoelectric cell are as – burglar alarm, Lux meter, exposure meter, solar cell, auto switches, reproduction of sound from cinefilm, TV cameras and - Safe Hands

Electron and Crook's tube • Recalls : • Force due to electric field E on charge q is given by qE • Force due to magnetic field of induction B on charge q moving with velocity v is given by qv X B • Crooks called phenomenon as gas discharge.At different pressures different phenomenon were observed.At 0.01mm of Hg crooks dark space fills the tube (exist from 1mm) and tube glows with green fluorescence. Safe Hands

• The name cathode ray was given by Goldstein • Sir J. J. Thompson found that cathode ray is stream of negatively charged bodies. • Milikan using oil drop model found the charge on electron. 1.6 x 10-19C

Eugen Goldstein

WilliamSafe Crookes Hands

Robert Millikan

Thompson’s experiment to determine e/m To determine e/m he used Crooks tube to deflect electron beam he used electric and perpendicular magnetic fields.The actual tube was as shown

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• When a vertically downward electric field is set the the electron will deviate in upward direction. • Due to a magnetic field pointing inward the electron will deflect in down ward direction if adjusting the magnitude of field we can bring back the spot. • Under above condition we have force due to electric field equals force due to magnetic field hence • eE = evB ⇒ v = E / B = V / d.B • Above value of v can be used for mv2 / r = evB hence e / m = v / rB • The value of r can be determined by following method Safe Hands

• Let there be only magnetic field applied then electron when enters the field will trace a circle and after leaving the field it will move along the tangent as shown.

r

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•As tangents are normal to radius we have two angles, A and B to be equal. •As angles are very small we have l/r = y /L •Hence

r = l L /y

•Thus e / m = v/rB will Echange to 

  E.y B  = 2  lL  lLB • e/m = .B y Safe Hands

L l

rr

y

• F = m.a = e.E hence a = (eE/m) • Y = 0 . t + ½ (eE/m) . t2 as vertical component is zero,of initial velocity. • t = v/L as horizontal component of velocity is constant. • Y = ½ (eE/m) . (v/L)2 Safe Hands • e/m = 2yL2/Ev2

Some points to remember • Specific charge of electron is 1.7589x1011C/kg

2eV e 11 = 2 V ≅ 2 V × 10 2 • eV = ½ mv hence v = m m • hν = mc2 hence Momentum of photon is mc = hν/c = h/ λ • Mass of photon = hν/c2 = h/ λ2 ν = h/cλ • Rest mass of photon is zero

m0any • According to special theory of relativity mass of object 2 v at rest if is m0 then mass at velocity v will be 1− c 2 Safe Hands