Which of the following sets of quantum numvber is not correctly represented in case of the indicated series of hydrogen atom ?

Options

A. Lyman series `n_(1) = 1, n_(2) = 2,3,4 …..`
B. balmer series `n_(1) = 2, n_(2) = 3,4,5 …..`
C. Paschen series `n_(1) = 1, n_(2) = 3,4,5 …..`
D. Brakett series `n_(1) = 4, n_(2) = 5,6,7 …..`

Answer

To determine which set of quantum numbers is incorrectly represented for the indicated series of the hydrogen atom, we need to analyze the quantum numbers associated with each series: Lyman, Balmer, Paschen, and Brackett.

### Step-by-Step Solution:

1. **Understanding Quantum Numbers**:
- In hydrogen, the quantum numbers are represented as:
- \( n_1 \): Principal quantum number of the lower energy level.
- \( n_2 \): Principal quantum number of the higher energy level.
- For a transition to occur, \( n_2 \) must be greater than \( n_1 \).

2. **Lyman Series**:
- The Lyman series involves transitions to the \( n_1 = 1 \) level.
- Possible values for \( n_2 \) are \( 2, 3, 4, \ldots \).
- This is correctly represented.

3. **Balmer Series**:
- The Balmer series involves transitions to the \( n_1 = 2 \) level.
- Possible values for \( n_2 \) are \( 3, 4, 5, 6, \ldots \).
- This is also correctly represented.

4. **Paschen Series**:
- The Paschen series involves transitions to the \( n_1 = 3 \) level.
- Possible values for \( n_2 \) are \( 4, 5, 6, \ldots \).
- If the set states \( n_1 = 1 \) and \( n_2 = 3 \), this is incorrect because \( n_1 \) cannot be 1 for the Paschen series.

5. **Brackett Series**:
- The Brackett series involves transitions to the \( n_1 = 4 \) level.
- Possible values for \( n_2 \) are \( 5, 6, 7, \ldots \).
- This is correctly represented.

6. **Conclusion**:
- The incorrect set of quantum numbers is for the Paschen series, where it was stated that \( n_1 = 1 \) and \( n_2 = 3 \). The correct representation should have \( n_1 = 3 \) and \( n_2 \) as \( 4, 5, 6, \ldots \).

### Final Answer:
The incorrect set of quantum numbers is for the Paschen series, where it should be \( n_1 = 3 \) and \( n_2 = 4, 5, 6, \ldots \).

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