Einstein Photoelectric Effect

7/27/2019 Einstein Photoelectric Effect

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PHOTOELECTRIC EFFECT

1. DEFINITION

2. EXPERIMENTAL SETUP

3. CHARACTERISTICS OF PHOTOELECTRIC EFFECT

4. EINSTEINS PHOTOELECTRIC EQUATION

h = wo + mvmax2 , wo = ho ,h = ho + mvmax

2

KEmax = vo .e , Vo = h - ho , vo = h / e - wo / e

Ref: Perspective of Modern Physics By Beiser

Modern Physics By Theraja


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PHOTO ELECTRIC EFFECT

DEFINITION

When radiation of suitable frequency

falls on a metal, electrons are emitted.This phenomenon is called PHOTOELECTRIC EFFECT.

In short, ejection of electrons frommatter by means of light is called 'photoelectric effect'.


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EXPERIMENTAL ARRANGEMENT TOOBSERVE PHOTOELECTRIC EFFECT


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1. If suitable light is allowed to fall onplate 'P', it will give out photo

electrons.2. The photo electrons are attracted by

the collector 'C' connected to the +veterminal of a battery.

3. The glass tube is evacuated.

4. When the collector 'C' is kept at +ve

potential, the photo electrons areattracted by it and a current flows inthe circuit which is indicated by thegalvanometer.


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THRESHOLD FREQUENCY

Threshold frequency is defined as the

minimum frequency of incident light whichcan cause photo electric emission

i.e. this frequency is just able to eject

electrons with out imparting K. E. to them

It is denoted by o .


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1. Minimum amount of energy which is

necessary to start photo electric emissionis called Work Function. If the amount ofenergy of incident radiation is less thanthe work function of the metal, no photo

electrons are emitted.

2. It is denoted by Wo.

3. It is a property of material. Differentmaterials have different values of workfunction. Generally, elements with low I.Pvalues have low work function such as Li,

Na, K, Rb, and Cs.

WORK FUNCTION


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STOPPING POTENTIAL

1. The negative potential of the plate 'C'

at which the photo electric currentbecomes zero is called stoppingpotential or cut-off potential.

2. Stopping potential is that value ofretarding potential differencebetween two plates which is justsufficient to halt the most energetic

photo electrons emitted.

3. It is denoted by "Vo".


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DEPENDENCE OF PHOTO ELECTRONS

The number of photo electrons dependsupon:

1. The nature of material

2. The frequency of incident radiation

3. The intensity of incident radiation


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EFFECT OF FREQUENCY

The graph shows that threshold frequencyis the minimum frequency below which noelectrons escape from the metal surface.

o

Vovmax


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EFFECT OF INTENSITY

The plot given below shows the photoelectric curves obtained by plotting photoelectric current 'I' versus collector voltage'V. It shows that there is a saturationcurrent for different intensities and even

when V=0, there is some photo electriccurrent .

The curve shows thatthe stopping potentialis independent of theintensity of radiation.


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If these curves are plotted for differentfrequencies 1 and 2 but with same

intensity the curve shows the behavior asshown:

The saturation

current depends uponintensity and not on

frequency.

However, the stoppingpotential becomesmore -ve from V01toVo2 with the increase

in frequency.


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FUNDAMENTAL LAWS OF PHOTOELECTRIC EMISSION

1. The no. of electrons emitted per secondwhich determines the saturation currentis proportional to the intensity of incidentlight.

2. There exists a threshold frequency belowwhich no photo electric emission takes

place.

3. The max. velocity or max. K.E ofphotoelectrons is independent of intensityand it varies directly with the frequency

of radiation.


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PHOTO- ELECTRIC EFFECT ON THE BASIS OFCLASSICAL ELECTRO- MAGNETIC THEORY OFMAXWELL

Process of transfer of energy from waves (of light) toparticles (electrons).

(a) The intensity of em waves varies as square of theamplitude and is independent of frequency

(b) The K.E of emitted electrons should be proportional tointensity and independent of frequency of incident light.

(c) Minimum intensity but not Frequency of light should

be necessary for the electrons to be emitted.

(d) The process of emission should be a time- delayedprocess depending on intensity of light, and cannot be

instantaneous.


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EINSTEIN'S PHOTOELECTRIC EQUATION

According to Plank's quantum theory,

light is emitted from a source in the form ofbundles of energy called photons. Energy ofeach photon is h.Einstein proposed that photons retain their

identity in space.

According to Einstein, when photons ofenergy fall on a metal surface, they transfer

their energy to the electrons of metal. Whenthe energy of photon is larger than theminimum energy required by the electronsto leave the metal surface, the emission of

electrons take place instantaneously.


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Thus the photonenergy is partly used

to liberate theelectron from thesurface of metal andthe balance energy

appears as the kineticenergy of emittedelectron. Distributionof K. E. is explained

by considering thedistribution of totalenergy of freeelectrons in a metal.

Ef=(h2/2m) (3n/8)2/3

EfWo=ho h

Max

K.E.

h

< MaxK. E.


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Equations from (1) to (6) are identical andare known as Einstein's photoelectricequations.


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SUMMARY

When light falls on metal, electrons are ejected frommetal, this is called Photo- electric Effect.

(i) The number of Photo electrons emitted from ametal is proportional to the Intensity of light but isindependent of the frequency of light.

(ii) The max K.E of emitted electrons is proportionalto the frequency of light and is independent of itsintensity.

(iii) Unless light of minimum frequency - dependingon the metal - is incident electrons are not ejected,for any intensity.

(iv) The ejection of electrons is always instantaneous.

Einstein Photoelectric Effect

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