The wave number of the series limit of Lyman series is -

Options

A. `1.097 xx 10^(7) m^(-1)`
B. `2.74 xx 10^(6) m^(-1)`
C. `1.22 xx 10^(6) m^(-1)`
D. `6.86 xx 10^(5) m^(-1)`

Explanation

To find the wave number of the series limit of the Lyman series, we can follow these steps:

### Step 1: Understand the Lyman Series
The Lyman series corresponds to the transitions of electrons in a hydrogen atom from higher energy levels (n ≥ 2) to the lowest energy level (n = 1). The series limit occurs when the electron transitions from an infinitely high energy level (n = ∞) to n = 1.

### Step 2: Use the Formula for Wave Number
The wave number (denoted as \( \bar{\nu} \)) is given by the formula:
\[ \bar{\nu} = \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where \( R_H \) is the Rydberg constant for hydrogen, \( n_1 \) is the lower energy level, and \( n_2 \) is the higher energy level.

### Step 3: Identify Values for the Lyman Series
For the Lyman series:
- \( n_1 = 1 \) (the lowest energy level)
- \( n_2 = \infty \) (the series limit)

### Step 4: Substitute the Values into the Formula
Substituting the values into the wave number formula:
\[ \bar{\nu} = R_H \left( \frac{1}{1^2} - \frac{1}{\infty^2} \right) \]
Since \( \frac{1}{\infty^2} = 0 \), the equation simplifies to:
\[ \bar{\nu} = R_H \left( 1 - 0 \right) = R_H \]

### Step 5: Use the Value of the Rydberg Constant
The Rydberg constant \( R_H \) is approximately:
\[ R_H = 1.097 \times 10^7 \, \text{m}^{-1} \]

### Step 6: Conclusion
Thus, the wave number of the series limit of the Lyman series is:
\[ \bar{\nu} = 1.097 \times 10^7 \, \text{m}^{-1} \]

### Final Answer
The wave number of the series limit of the Lyman series is \( 1.097 \times 10^7 \, \text{m}^{-1} \).