#### Assertion: The kinetic energy of photoelectrons depends on the frequency of incident radiation.Reason: The kinetic energy of photoelectrons is determined by the difference between the energy of the incident photon and the work function of the metal.Option: 1 Both assertion and reason are true, and the reason is the correct explanation of the assertion.  Option: 2 Both assertion and reason are true, but the reason is not the correct explanation of the assertion.  Option: 3 Assertion is true, but the reason is false.  Option: 4 Assertion is false, but the reason is true.

The kinetic energy of photoelectrons is given by the equation:

$k_{\max }=\frac{1}{2} m v_{\max }^2=h \nu-\phi$

where, $m$ is the mass of the photoelectron, $v_{\max }$ is the maximum velocity of the emitted electron, h is the Planck's constant,and  $\nu$ is the frequency of the incident radiation.

Thus, the kinetic energy of the photoelectrons depends on the frequency of the incident radiation. The higher the frequency of the incident radiation, the higher the energy of the emitted electrons.

The reason given is also correct. The amount of energy needed at least to remove an electron from the surface of a metal is represented by the work function. If the energy of the incident photon is less than the work function, no photoelectrons are emitted. Thus, the kinetic energy of photoelectrons is determined by the difference between the energy of the incident photon and the work function of the metal.

Therefore, option 1 is the correct answer.