Physics - Modern Physics Question with Solution | TestHub

According to Einstein's photoelectric equation, the maximum kinetic energy of emitted photoelectrons is given by $K=E-W$, where $E$ is the energy of incident photons and $W$ is the work function.

For the first case, $E_1=4W$.

$K_1=4W-W=3W$

For the second case, $E_2=6W$.

$K_2=6W-W=5W$

Since kinetic energy $K=\frac{1}{2}m{v}^2$, the velocity $v$ is proportional to $\sqrt{K}$.

The ratio of velocities is $\frac{v_1}{v_2}=\sqrt{\frac{K_1}{K_2}}=\sqrt{\frac{3W}{5W}}=\frac{\sqrt{3}}{\sqrt{5}}$.

Thus, the ratio is $\sqrt{3}:\sqrt{5}$.

Answer: $\sqrt{3}:\sqrt{5}$