Work function $\left(W_0\right)$ values of six metals (in $\mathrm{eV}$ ) are given below. $\mathrm{Li}…
Work function $\left(W_0\right)$ values of six metals (in $\mathrm{eV}$ ) are given below.
$\mathrm{Li} \quad \mathrm{Mg} \quad \mathrm{Cu} \quad \mathrm{Ag} \quad \mathrm{K} \quad \mathrm{Na}$
$\begin{array}{llllll}2.42 & 3.7 & 4.8 & 4.3 & 2.25 & 2.3\end{array}$
How many of the above metals do not eject the electrons when they are made to strike with radiation of wavelength $400 \mathrm{~nm}$ ?
$$
\left(h=6.62 \times 10^{-34} \mathrm{Js}\right)
$$
$4$
$2$
$3$
$5$
Solution
Energy of radiation of wavelength $400 \mathrm{~nm}$
$
\begin{aligned}
& \text { ( } \mathrm{nm}=10^{-9} \mathrm{~m} \text { ) } \\
& E=\frac{h c}{\lambda}=\frac{6.6 \times 10^{-34} \mathrm{Js} \times 3.0 \times 10^8 \mathrm{~ms}^{-1}}{400 \times 10^{-9} \mathrm{~m}} \\
& =4.95 \times 10^{-19} \mathrm{~J} \\
&
\end{aligned}
$
Now, $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$
$
\begin{aligned}
\therefore \quad E & =\frac{4.95 \times 10^{-19}}{1.6 \times 10^{-19}} \\
& =3.09 \mathrm{eV}
\end{aligned}
$
Since, work function of three metals $\mathrm{Mg}, \mathrm{Cu}$ and $\mathrm{Ag}$ is larger than $3.09 \mathrm{eV}$, so these metals will not eject electrons on striking with radiation of wavelength $400 \mathrm{~nm}$