Use Einstein’s photoelectric equation

The maximum kinetic energy of emitted photoelectrons is $K_{\max}=h\nu-\phi$ where:

• $h\nu$ = energy of incident photon
• $\phi$ = work function of the metal

Check Assertion A

Assertion A says:

The photoelectric effect does not take place if the energy of the incident radiation is less than the work function of a metal.

If $h\nu<\phi,$ then $K_{\max}=h\nu-\phi<0$ which is not physically possible for emitted electrons. Hence, no photoelectrons are emitted.

So, Assertion A is correct.

Check Reason R

Reason R says:

Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.

If $h\nu=\phi,$ then from Einstein’s equation, $K_{\max}=h\nu-\phi=0$

So, Reason R is also correct.

Does R correctly explain A?

Reason R only tells us what happens at the threshold condition: $h\nu=\phi \Rightarrow K_{\max}=0$

But Assertion A is about the case $h\nu<\phi$ where emission does not occur.

While both statements are true, R does not directly explain why no photoelectric effect occurs for photon energy less than the work function. It only states the threshold case.

Conclusion

• A is correct
• R is correct
• R is not the correct explanation of A

Therefore, the correct option is: $\boxed{\text{B}}$