Question

What is the work function of the metal?

• A. $6.86eV$
• B. $3.6eV$
• C. $5.4eV$
• D. $6.25eV$

Answer 1

Answer: (A)

$6.86eV$

In the first case:

Using photoelectric equation, we have
$\Rightarrow 13.6=h\nu -W$

where, W is the work function.
In the second case:
$\Rightarrow \frac{hc}{\lambda }=\frac{5h\nu }{6}-W$
$\Rightarrow \frac{hc}{\lambda }=\frac{66\times {10}^{-34}\times 3\times {10}^8}{1215\times {10}^{-10}}$
$=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{1215\times {10}^{-10}\times 1.6\times {10}^{-19}}$
$=10.19eV$
$\Rightarrow \frac{5h\nu }{6}=W+10.19$
We know that: $h\nu =W+13.6$
$\Rightarrow \frac{h\nu }{6}=3.41$
$\Rightarrow h\nu =3.41\times 6$
Therefore, Workfunction, $W=3.41\times 6-13.6$
$=20.46-13.6=6.86eV$
$\therefore$ Work function of metal $=6.86eV$