According to Bohr's frequency rule (Source , Eq 2.10), the frequency of radiation absorbed or emitted during a transition is given by $\nu = \Delta E / h$. Here, the incident radiation has frequency $\nu = (E_2 - E_1)/h$, which corresponds exactly to the energy gap between the ground state ($n=1$) and the first excited state ($n=2$). Therefore, the atoms can absorb this energy and transition to the $n=2$ state . Statement (a) is incorrect because absorption occurs. Statement (c) is incorrect because the interaction is probabilistic; not all atoms absorb photons simultaneously. Statement (d) is correct because the energy is insufficient to bridge the gap to $n=3$ ($E_3 - E_1$), and quantized transitions require specific energies . Thus, statements (b) and (d) are correct.