The work function of a metal $M$ is $6.3 \mathrm{eV}$. The wavelength of the incident radiation required to…
The work function of a metal $M$ is $6.3 \mathrm{eV}$. The wavelength of the incident radiation required to just eject the electrons from its surface (in $\mathrm{nm}$ ) is
$102$
$330$
$197$
$310$
Solution
The work function of the metal $M$ is $6.3 \mathrm{eV}$.
$
\begin{aligned}
1 \mathrm{eV} & =1.6 \times 10^{-19} \mathrm{~J} \\
E & =6.3 \times 1.6 \times 10^{-19} \mathrm{~J} \\
& =10.08 \times 10^{-19} \mathrm{~J}
\end{aligned}
$
The wavelength of radiation can be calculated. Using the formula,
$
\begin{aligned}
E & =\frac{h c}{\lambda} \\
\lambda & =\frac{h c}{E}=\frac{6.6 \times 10^{-34} \mathrm{Js} \times 3.0 \times 10^8 \mathrm{~ms}^{-1}}{10.08 \times 10^{-19} \mathrm{~J}} \\
& =1.9642 \times 10^{-7} \mathrm{~m} \\
& =197 \mathrm{~nm}
\end{aligned}
$