Let En = -(me^4)/(8ε_0^2 n^2 h^2) be the energy of the nth level of H-atom. If all the H-atoms are in the grou

Question

Let En = -(me^4)/(8ε_0^2 n^2 h^2) be the energy of the nth level of H-atom. If all the H-atoms are in the ground state and radiation of frequency (E2 - E1)/h falls on it, then:
(a) it will not be absorbed at all.
(b) some of the atoms will move to the first excited state.
(c) all atoms will be excited to the n=2 state.
(d) no atoms will make a transition to the n=3 state.

Choose the correct option:

Accepted Answer

According to Bohr's frequency rule (Source , Eq 2.10), the frequency of radiation absorbed or emitted during a transition is given by $
u = \Delta E / h$. Here, the incident radiation has frequency $
u = (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.

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