Step 1: Calculate Maximum Kinetic Energy ($K_{max}$): Einstein's equation is: $K_{max} = E - \phi$, where $E$ is photon energy and $\phi$ is the work function.
• For the first photon ($E_1 = 2.5 \text{ eV}$):
$$K_1 = 2.5 - 1.5 = 1.0 \text{ eV}$$
• For the second photon ($E_2 = 3.5 \text{ eV}$):
$$K_2 = 3.5 - 1.5 = 2.0 \text{ eV}$$
Step 2: Relate Kinetic Energy to Velocity: Kinetic energy is given by $K = \frac{1}{2}mv^2$. Therefore, velocity $v \propto \sqrt{K}$.
The ratio of maximum velocities is:
$$\frac{v_1}{v_2} = \sqrt{\frac{K_1}{K_2}}\lt strong\gt Step 3: Calculate the Ratio\lt /strong\gt \frac{v_1}{v_2} = \sqrt{\frac{1.0}{2.0}} = \frac{1}{\sqrt{2}}$$
$$\text{Ratio} = 1 : \sqrt{2}$$