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)

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 $