Q: Cut off potentials for a metal in photoelectric effect for light of wavelength λ1 , λ2 and λ3 is found to be V1 , V2 and V3 volts if V1 , V2 and V3 are in Arithmetic Progression then λ1 , λ2 and λ3 will be :
(A) Arithmetic Progression
(B) Geometric Progression
(C) Harmonic Progression
(D) None
Solution :
$\large \frac{hc}{\lambda_1} = \phi + e V_1 $
$\large \frac{hc}{\lambda_2} = \phi + e V_2 $
$\large \frac{hc}{\lambda_3} = \phi + e V_3 $
As V1 , V2 and V3 are in Arithmetic Progression .
φ + e V1 , φ + e V2 and φ + e V3 are also in Arithmetic Progression .
$\large \frac{hc}{\lambda_1} , \frac{hc}{\lambda_2} , \frac{hc}{\lambda_3} $ are in A.P
$\large \frac{1}{\lambda_1} , \frac{1}{\lambda_2} , \frac{1}{\lambda_3} $ are in A.P
Therefore , λ1 , λ2 and λ3 will be in H.P
correct option is (C)