Physics - Modern Physics Question with Solution | TestHub

Let the work function of the metal be $\Phi$.

The energy of the first photon is $E_1=2\Phi$ and the energy of the second photon is $E_2=3\Phi$.

According to Einstein's photoelectric equation, the maximum kinetic energy is given by $K_{max}=E-\Phi$.

For the first photon:
$K_{max1}=2\Phi -\Phi =\Phi$

For the second photon:
$K_{max2}=3\Phi -\Phi =2\Phi$

The maximum kinetic energy is related to the maximum velocity by $K_{max}=\frac{1}{2}m{v}_{max}^2$.

Taking the ratio of the kinetic energies:
$\frac{K_{max1}}{K_{max2}}=\frac{\frac{1}{2}m{v}_{max1}^2}{\frac{1}{2}m{v}_{max2}^2}=\frac{\Phi }{2\Phi }$

$\frac{v_{max1}^2}{v_{max2}^2}=\frac{1}{2}$

$\frac{v_{max1}}{v_{max2}}=\frac{1}{\sqrt{2}}$

The ratio of maximum velocities is $1:\sqrt{2}$.

Answer: $1:\sqrt{2}$