The maximum velocity of an electron emitted by light of wavelength \(\lambda\) incident on the surface of a…
The maximum velocity of an electron emitted by light of wavelength \(\lambda\) incident on the surface of a metal of work function \(\phi\) is [ \(h=\) Planck's constant, \(m=\) mass of electron and \(c=\) speed of light]
\(\sqrt{\frac{2(h c+\lambda \phi)}{m \lambda}}\)
\(\frac{2(h c-\lambda \phi)}{m}\)
\(\sqrt{\frac{2(h c-\lambda \phi)}{m \lambda}}\)
\(\frac{2(h \lambda-\phi)}{m}\)
Solution
According to Einstein's photoelectric equation, maximum kinetic energy of emitted electron is
\(\begin{aligned}
& K_{\max }=\frac{h c}{\lambda}-\phi \quad \Rightarrow \frac{1}{2} m v_{\max }^2=\frac{h c-\lambda \phi}{\lambda} \\
& \Rightarrow \quad v_{\max }^2=\frac{2(h c-\lambda \phi)}{m \lambda} \Rightarrow v_{\max }=\sqrt{\frac{2(h c-\lambda \phi)}{m \lambda}}
\end{aligned}\)