A photosensitive metallic surface has work function \(\phi\). If photon of energy \(3 \phi\) falls on the surface, the electron comes out with a maximum velocity of \(6 \times 10^6 \mathrm{~m} / \mathrm{s}\). When the photon energy is increased to \(9 \phi\), then maximum velocity of photoelectrons will be

\(\begin{aligned}
& \text { For photoelèctric effect, } \\
& \mathrm{K} . \mathrm{E}_{\max }=\mathrm{E}-\phi_0 \\
& \text { Given: } E_1=3 \phi_0 \text { and } E_2=9 \phi_0 \\
& \text { From (i), } \\
& K . E_1=3 \phi_0-\phi_0=2 \phi_0 \\
& K . E_2=9 \phi_0-\phi_0=8 \phi_0 \text {. } \\
& \text { But, } K \cdot E_1=\frac{1}{2} \mathrm{mv}_1^2 \text { and } \mathrm{K} \cdot \mathrm{E}_2=\frac{1}{2} \mathrm{mv}_2^2 \\
& \therefore \quad \frac{\mathrm{~K} \cdot \mathrm{E}_1}{\mathrm{~K} \cdot \mathrm{E}_2}=\frac{\mathrm{v}_1^2}{\mathrm{v}_2^2}=\frac{1}{4} \\
& \therefore \quad \mathrm{v}_2=2 \mathrm{v}_1 \\
& \mathrm{v}_2=2 \times 6 \times 10^6=12 \times 10^6 \mathrm{~m} / \mathrm{s}
\end{aligned}\)