Question

Light of wavelength $λ_A$ and $λ_B$ falls on two identical metal plates $A$ and $B$ respectively. The maximum kinetic energy of photoelectrons in $K_A$ and $K_B$ respectively, then which one of the following relations is true ? $(λ_A = 2\, λ_B)$

• A. $K_{A} < \frac{K_{B}}{2}$
• B. $2\,K_{A} = K_{B}$
• C. $K_{A} =2\, K_{B}$
• D. $K_{A} > 2\, K_{B}$

Answer 1

Answer: (A)

According to Einstein photoelectric equation
$K_{A}=\frac{h c}{\lambda_{A}}-\phi \Rightarrow 2 K_{A}=\frac{2 h c}{\lambda_{A}}-2 \phi$
or $\,\,\,2 K_{A}+\phi=\frac{2 h c}{\lambda_{A}}-\phi$
Wavelength of metal $B$ is half of metal $A$
$\therefore \,\,\,2 K_{A}+\phi =K_{B} $
$\Rightarrow K_{A} <\frac{K_{B}}{2}$