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

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)