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 = $h{v}_0=\frac{hc}{{\lambda }_0}$
where, ${\lambda }_0$ is the threshold wavelength.
or $W_0\propto \frac{1}{{\lambda }_0}$
$\therefore \frac{W_0}{W_0^{\prime }}=\frac{{\lambda }_0^{\prime }}{{\lambda }_0}$
or $\frac{W_0}{(W_0/2)}=\frac{{\lambda }_0^{\prime }}{{\lambda }_0}$
$\Rightarrow {\lambda }_0^{\prime }=2{\lambda }_0$