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Light of frequency $7.21 \times 10^{14} \mathrm{~Hz}$ is incident on a metal surface. Electrons with a maximum speed of $6.0 \times 10^5 \mathrm{~m} / \mathrm{s}$ are ejected from the surface. What is the threshold frequency for photoemission of electrons?
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Verified Answer
Given: $v=7.21 \times 10^{14} \mathrm{HZ}, \mathrm{V}_{\max }=6.0 \times 10^5 \mathrm{~m} / \mathrm{s}$
By Einsteins equation $\mathrm{hv}=\mathrm{hv} v_0+\frac{1}{2} \mathrm{mv}_{\max }^2$
$$
\begin{aligned}
&\Rightarrow v_0=v-\frac{\mathrm{mv}_{\max }^2}{2 \mathrm{~h}} \\
&=7.21 \times 10^{14}-\frac{9.1 \times 10^{-31} \times\left(6.0 \times 10^5\right)^2}{2 \times 6.6 \times 10^{-34}} \\
&=7.21 \times 10^{14}-2.47 \times 10^{14}=4.74 \times 10^{14} \mathrm{~Hz}
\end{aligned}
$$
By Einsteins equation $\mathrm{hv}=\mathrm{hv} v_0+\frac{1}{2} \mathrm{mv}_{\max }^2$
$$
\begin{aligned}
&\Rightarrow v_0=v-\frac{\mathrm{mv}_{\max }^2}{2 \mathrm{~h}} \\
&=7.21 \times 10^{14}-\frac{9.1 \times 10^{-31} \times\left(6.0 \times 10^5\right)^2}{2 \times 6.6 \times 10^{-34}} \\
&=7.21 \times 10^{14}-2.47 \times 10^{14}=4.74 \times 10^{14} \mathrm{~Hz}
\end{aligned}
$$
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