Q.

Light of wavelength λph  falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is ϕ and the anode is a wire mesh of conducting material kept at a distance d  from the cathode. A potential difference V  is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is λe,  which of the following statements(s) is (are) true?

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a

For large potential difference Vϕ/e,λe  is approximately halved if V  is made  four times.
 

b

λeis approximately halved, if  d is doubled

c

λeincreases at the same rate as λph  for  λph<hc/ϕ

d

λedecreases with increase in ϕ  and λph 

answer is D.

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Detailed Solution

Kmax=hcλphϕ

Kinetic energy of electron reaching the anode will be
K=hcλphϕ+eV 
Now,  λe=h2mK=h2m hvλphϕ+eV
If eV>>ϕ  then,
 λe=h2mhcλph+eV
If,  Vf=4Vi then,
λefλei2

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