Question

The threshold wavelength for a metal with work function $W_0$ is ${\lambda }_0$. What is the threshold wavelength for a metal whose work function is $\frac{W_0}{2}$?

• A. $\frac{{\lambda }_0}{4}$
• B. $\frac{{\lambda }_0}{2}$
• C. $2{\lambda }_0$
• D. $4{\lambda }_0$

Answer 1

The correct option is C $2{\lambda }_0$

For a metal of work function $W_0$, $W_0=\frac{hc}{{\lambda }_0}$
Now, for a metal of work function $\frac{W_0}{2}$, $\frac{W_0}{2}=\frac{hc}{\lambda }$
$\Rightarrow \frac{hc}{2{\lambda }_0}=\frac{hc}{\lambda }\Rightarrow \lambda =2{\lambda }_0$
Hence, the correct choice is (c).