Q: The graph between the stopping potential (V0) and (1/λ) is shown in figure, φ_{1 }, φ_{2} and φ_{3} are work functions. Which of the following is correct

(a)φ_{1 }:φ_{2 }:φ_{3 } = 1 : 2 : 4

(b) φ_{1 }:φ_{2 }:φ_{3 } = 4 : 2 : 1

(c) tan θ is directly proportional to hc/e, where h is Planck’s constant and c is the speed of light

(d) ultraviolet light can be used to emit photoelectrons from metal 2 and meal 3 only.

Ans: (a)

Sol:

$ \displaystyle \frac{hc}{\lambda} = \phi + eV_0 $

$ \displaystyle V_0 = \frac{hc}{e \lambda}- \frac{\phi}{e} $

When λ = λ_{0} , K.E = 0

$ \displaystyle \frac{hc}{\lambda_0} = \phi $

$ \displaystyle \frac{\phi}{hc} = \frac{1}{\lambda_0} $

$ \displaystyle \frac{\phi_1}{hc} = 0.001 $

$ \displaystyle \frac{\phi_2}{hc} = 0.002 $

$ \displaystyle \frac{\phi_3}{hc} = 0.004 $

φ_{1 }:φ_{2 }:φ_{3 } = 1 : 2 : 4