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Illustrations

Example-1

A photon of frequency 5 × 1014 Hz is incident on the surface of a metal. If the photoelectric threshold frequency for the metal is 3 × 1014 Hz, calculate

  1. the energy of the photon
  2. the photoelectric work function in eV.
Solution
  1. Energy of the photon, E = hv
     
    h = 6.625 × 10–34 J s, v = 5 × 1014 Hz
     
    ∴ E = (6.625 ×10–34 × 5 × 1014)
     
    1.6 × 10–19 J = 1 eV
     
    ∴ E = Description: 39367.png eV
     
    Description: 39378.png
     
    = 2.07 eV.
  2. Photoelectric work function
     
    W = hv0
     
    = (6.625 × 10-34 × 3 × 1014) J
     
    Description: 39392.png
     
    i.e., W = 1.24 eV.


Example-2

The threshold wavelength for a metal is 680 nm. Calculate the maximum velocity of photoelectrons emitted, when radiation of wavelength 560 nm is incident on the metal.

Solution

Threshold wavelength is λ0 = 680 nm = 680 × 10–9 m.

 

We know from Einstein’s equation

 

E = W + T (T is the kinetic energy of the electrons)
T = E – W

 

but E = hv and W = hv0

 

∴ T = hv − hv0 (1)

 

But Description: 39407.png, where ‘c’ is the velocity of light. Therefore, Eq. (1) becomes

 

Description: 39415.png

 

Description: 39422.png

 

= 6.625 × 10–34 × 3 × 108 × Description: 39430.png

 

= 6.26 × 10–20 J.
 





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