Question

The threshold wavelength for a metal having work function $W_0$ is $\lambda_0$. What is the threshold wavelength for a metal whose work function is $\frac{ W_0 }{ 2 }$ ?

• A. $4 \lambda_0$
• B. $2 \lambda_0$
• C. $\frac{ \lambda_0 }{ 2}$
• D. $\frac{ \lambda_0 }{ 4}$

Answer 1

Answer: (B)

$2 \lambda_0$

Answer 2

Work function of a metal is given by W = $hv_0 = \frac{ h c }{ \lambda_0 }$ where, $\lambda_0$ is the threshold wavelength. or $W_0 \propto \frac{ 1}{ \lambda_0 }$ $\therefore \frac{ W_0 }{ W_0' } = \frac{ \lambda_0 ' }{ \lambda_0 }$ or $\frac{ W_0 }{ ( W_0 / 2 ) } = \frac{ \lambda_0 ' }{ \lambda_0 }$ $\Rightarrow \lambda_0 ' = 2 \lambda_0$