Dual Nature of radiation and matter part 02

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Hey friends, In this blog you will understand expression for the maximum K.E of Photoelectrons, Effect on stopping potential of frequency, laws of photoelectric effect, Einstein's photoelectric equation, De - Broglie wave equation, De - broglie wavelength for an electron, and Determination of planck's constant & work function. 


Dual nature of radiation and matter part 02



Expression for maximum kinetic energy of Photoelectrons


The amount of work done to restrict the electrons having maximum kinetic energy

W = (K.E)max    .... (1) 

W. K. T 
   
Vo = W/e

W = eVo

From (1) 

(K.E)max = eVo

(1/2)×m(vmax × vmax) = eVo

Where, vmax = maximum velocity


Effect on stopping potential of frequency












 • The stopping potential is directly proportional to the frequency of incident radiation. 

• The K.E of Photoelectrons increases with 
    frequency of incident radiation. 


Laws of photo electric effect

(1). The photo electric current is directly proportional to the intensity of incident radiation & no. of Photoelectrons. 

(2). The minimum frequency below which the Photoelectrons do not emit from metal surface is known as threshold frequency, denoted by vo. 

(3). Stopping potential is directly proportional to the maximum K.E of Photoelectrons. 

(4). Photoelectric effect is an instantaneous effect the time lags between incident radiation and originating Photoelectrons is very small. 
For ex - 10(of power of -9 seconds) 

Einstein's photoelectric equation

Consider a metal sheet on which the radiation strikes Einstein suggested that one photon interacts with individual electrons of the substance. 

Acc. To Einstein, the energy of incident photon is used in two ways first as work function energy to liberate electrons on the surface or inside the metal coming out from the metal  and the other part is used to give maximum K.E to the Photoelectrons. 














Energy of photon = work function + (K.E)max   .... (1) 

W. K. T

Energy of photon = hv 
And
Work function energy = hvo
And
(K.E)max = (1/2)m×(vmax)×(vmax) 

From (1) 

hv = hvo + (1/2)m×(vmax) × (vmax) 

(1/2) m × (vmax) × (vmax) = hv - hvo = h(v - vo) 

This is the Einstein's photoelectric equation. 

                           Outcomes


• The minimum frequency below which the electrons do not emit from the metal surface is known as threshold frequency (vo) 

• if v is smaller than vo

Then,  (1/2) m×(vmax) × (vmax) = negative

This is not possible
Therefore, no Photoelectrons are emitted from metal surface. 

Hence, no photoelectric effect is obtained. 


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