Q: Cut off potentials for a metal in photoelectric effect for light of wavelength λ_{1} , λ_{2} and λ_{3} is found to be V_{1} , V_{2} and V_{3} volts if V_{1} , V_{2} and V_{3} are in Arithmetic Progression then λ_{1} , λ_{2} and λ_{3} 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 V_{1} , V_{2} and V_{3} are in Arithmetic Progression .

φ + e V_{1} , φ + e V_{2} and φ + e V_{3} 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 , λ_{1} , λ_{2} and λ_{3} will be in H.P

correct option is (C)