Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The photoelectric effect does not take place, if the energy of the incident radiation is less than the work function of a metal.
Reason R: Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.

Einstein’s photoelectric equation is stated first:
$$K_{\text{max}} = h\nu - \phi \quad -(1)$$ where $$K_{\text{max}}$$ is the maximum kinetic energy of emitted electrons, $$h$$ is Planck’s constant, $$\nu$$ is the frequency of incident radiation, and $$\phi$$ is the work function of the metal.

For photoelectric emission to occur, we require $$K_{\text{max}} \gt 0$$. From (1):
$$h\nu - \phi \gt 0 \quad\Longrightarrow\quad h\nu \gt \phi$$ If $$h\nu \lt \phi$$ then $$K_{\text{max}} \lt 0$$, which is not physically possible. Hence no electrons are emitted and the photoelectric effect does not take place. This shows Assertion A is correct.

Next consider the case $$h\nu = \phi$$. Substituting into (1) gives:
$$K_{\text{max}} = \phi - \phi = 0$$ This means that at the threshold frequency, electrons are just emitted with zero kinetic energy. Therefore Reason R is also correct.

However, Reason R describes the situation exactly at $$h\nu = \phi$$ and does not explain why emission fails when $$h\nu \lt \phi$$. Thus R is not the correct explanation of A.

Final answer: Both A and R are correct but R is not the correct explanation of A (Option B).