The work functions $\left(W_0\right)$ of $\mathrm{K}, \mathrm{Na}, \mathrm{Li}, \mathrm{Mg}$ and…
The work functions $\left(W_0\right)$ of $\mathrm{K}, \mathrm{Na}, \mathrm{Li}, \mathrm{Mg}$ and $\mathrm{Cu}$ are $2.25,2.30,2.42,3.70$ and $4.80 \mathrm{eV}$ respectively. How many of these metals do not undergo photoelectric effect when a radiation of wavelength $450 \mathrm{~nm}$ is allowed to fall on them? $\left(1 \mathrm{eV}=1.602 \times 10^{-19} \mathrm{~J}\right)$
2
1
3
5
Solution
$
\begin{aligned}
& \lambda=450 \mathrm{~nm} \\
& E=h v
\end{aligned}
$
or
$
\begin{aligned}
E & =h \frac{c}{\lambda} \Rightarrow 6.6 \times 10^{-34} \mathrm{Js} \times \frac{3 \times 10^8 \mathrm{~m} / \mathrm{s}}{450 \times 10^{-9} \mathrm{~m}} \\
E & =0.044 \times 10^{-17} \text { or } 4.4 \times 10^{-19} \mathrm{~J} \\
E & =\frac{4.4 \times 10^{-19}}{1.602 \times 10^{-19}}=2.74 \mathrm{eV} \\
& {\left[\because 1 \mathrm{eV}=1.602 \times 10^{-19}\right] }
\end{aligned}
$
Thus, K, Na and Li, which have less value of work functions $\left(W_0\right)$ than the energy of striking photon $(E)$, so can undergo photoelectric effect when radiation of wavelength $450 \mathrm{~nm}$ is allowed to fall on them