In unielectron system, the wave number of any spectral line is directly proportional to

Options

A. the number of particles present in the system
B. the velocity of electron undergoing transition
C. `(1)/(n_(1)^(2))-(1)/(n_(2)^(2))`
D. the charge on the nucleus and the `lambda` of light used.

Explanation

To solve the question regarding the relationship of wave number in a unielectron system, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Unielectron System**:
- A unielectron system refers to atoms or ions that have only one electron. Examples include hydrogen (H), helium ion (He+), and lithium ion (Li2+).

2. **Wave Number Definition**:
- The wave number (denoted as \( \bar{\nu} \)) is defined as the number of wave cycles per unit distance. It is often expressed in reciprocal centimeters (cm⁻¹).

3. **Formula for Wave Number**:
- For a unielectron system, the wave number can be expressed using the formula:
\[ \bar{\nu} = Z^2 R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where:
- \( Z \) is the atomic number,
- \( R \) is the Rydberg constant,
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final energy levels, respectively.

4. **Analyzing Proportionality**:
- From the formula, we can see that the wave number \( \bar{\nu} \) is directly proportional to \( Z^2 \) and the term \( \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \).
- This indicates that the wave number is influenced by the atomic number \( Z \) and the quantum states involved in the transition.

5. **Conclusion**:
- Therefore, in the context of the question, the wave number of any spectral line in a unielectron system is directly proportional to the term \( \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), which relates to the energy transitions between the quantum levels.

### Final Answer:
The wave number of any spectral line in a unielectron system is directly proportional to \( \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \).

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