A hydrogen atom in an excited state emits a photon which has the longest wavelength of the Paschen series . Further emissions from the atom cannot include the :

Options

A. longest wavelength of the Lyman series
B. second longest wavelength of the Lyman series
C. longest wavelength of the Balmer series
D. second longest wavelength of the Balmer series

Answer

To solve the problem, we need to understand the Paschen series in the context of the hydrogen atom and the implications of an atom emitting a photon with the longest wavelength in this series.

### Step-by-Step Solution:

1. **Understanding the Paschen Series**:
- The Paschen series corresponds to electronic transitions in a hydrogen atom where the electron falls to the n=3 energy level from higher energy levels (n=4, n=5, etc.).
- The wavelengths of the emitted photons in the Paschen series are in the infrared region.

2. **Identifying the Longest Wavelength**:
- The longest wavelength in the Paschen series occurs when the transition is from n=4 to n=3. This is because longer wavelengths correspond to smaller energy differences between the energy levels.
- The formula for the wavelength (λ) of the emitted photon can be derived from the Rydberg formula:
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where \( R_H \) is the Rydberg constant, \( n_1 = 3 \), and \( n_2 = 4 \).

3. **Emissions After the Longest Wavelength**:
- Once the hydrogen atom emits a photon with the longest wavelength (from n=4 to n=3), it will be in the n=3 state.
- The possible transitions from n=3 are:
- n=3 to n=2 (visible region)
- n=3 to n=1 (ultraviolet region)

4. **Identifying Forbidden Transitions**:
- After the transition to n=3, the hydrogen atom cannot emit a photon that corresponds to a transition to a level higher than n=3, as it is already in the n=3 state.
- Therefore, transitions to n=4 or higher (n=5, n=6, etc.) are not possible as the atom cannot absorb energy to go to a higher state after emitting the photon.

5. **Conclusion**:
- The answer to the question is that further emissions from the atom cannot include transitions to levels higher than n=3 (i.e., n=4 or higher).

### Final Answer:
Further emissions from the atom cannot include transitions to n=4 or higher.