Given below are two statements: one is labelled as Assertion (A)...

Reason (R) is correct: According to Bohr's model, the kinetic energy of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is $K = \dfrac{13.6}{n^2} \text{ eV}$. Thus, $K \propto \dfrac{1}{n^2}$.

Assertion (A) is correct: The first excited state corresponds to the principal quantum number $n_1 = 2$, and the third excited state corresponds to $n_2 = 4$.

Using the relation from the Reason:
$K_1 \propto \dfrac{1}{2^2} = \dfrac{1}{4}$
$K_2 \propto \dfrac{1}{4^2} = \dfrac{1}{16}$

The ratio of their kinetic energies is $\dfrac{K_1}{K_2} = \dfrac{1/4}{1/16} = 4$.
Therefore, the kinetic energy in the first excited state is four times that in the third excited state.

Since the inverse-square relationship directly leads to the calculated ratio, (R) is the correct explanation of (A).

Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)