The limiting value of wave number in Lyman series of hydrogen atoms is:

Answer

To find the limiting value of the wave number in the Lyman series of hydrogen atoms, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Lyman Series**: The Lyman series corresponds to electronic transitions in a hydrogen atom where the electron falls to the n=1 energy level from higher energy levels (n=2, 3, 4, ...).

2. **Use the Rydberg Formula**: The Rydberg formula for the wave number (1/λ) is given by:
\[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where \( R \) is the Rydberg constant, \( n_1 \) is the lower energy level, and \( n_2 \) is the higher energy level.

3. **Identify the Values for Lyman Series**: For the Lyman series, the lower energy level \( n_1 \) is 1. The higher energy level \( n_2 \) can go to infinity for the limiting case.

4. **Substitute the Values**: Substitute \( n_1 = 1 \) and \( n_2 = \infty \) into the Rydberg formula:
\[ \frac{1}{\lambda} = R \left( \frac{1}{1^2} - \frac{1}{\infty^2} \right) \]

5. **Evaluate the Expression**: Since \( \frac{1}{\infty^2} = 0 \), the equation simplifies to:
\[ \frac{1}{\lambda} = R \left( 1 - 0 \right) = R \]

6. **Substitute the Rydberg Constant**: The value of the Rydberg constant \( R \) is approximately \( 1.097 \times 10^7 \, \text{m}^{-1} \) or \( 109678 \, \text{cm}^{-1} \).

7. **Conclusion**: Therefore, the limiting value of the wave number in the Lyman series of hydrogen atoms is:
\[ \frac{1}{\lambda} = 109678 \, \text{cm}^{-1} \]

### Final Answer:
The limiting value of wave number in the Lyman series of hydrogen atoms is \( 109678 \, \text{cm}^{-1} \).

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