Given the value of Rydberg constant is `10^(7)m^(-1)`, the waves number of the last line of the Balmer series in hydrogen spectrum will be:

Options

A. `0.5xx10^(7) m^(-1)`
B. `0.25xx10^(7) m^(-1)`
C. `2.5xx10^(7) m^(-1)`
D. `0.025xx10^(4) m^(-1)`

Explanation

To find the wave number of the last line of the Balmer series in the hydrogen spectrum, we can follow these steps:

### Step 1: Understand the formula for wave number
The wave number (denoted as \( \bar{\nu} \)) is given by the formula:
\[ \bar{\nu} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \]
where:
- \( R \) is the Rydberg constant,
- \( n_f \) is the final energy level,
- \( n_i \) is the initial energy level.

### Step 2: Identify the values for the Balmer series
For the Balmer series:
- The final energy level \( n_f \) is always 2.
- The last line of the Balmer series corresponds to the transition from \( n_i = \infty \) to \( n_f = 2 \).

### Step 3: Substitute the values into the formula
Substituting \( n_f = 2 \) and \( n_i = \infty \) into the wave number formula:
\[ \bar{\nu} = R \left( \frac{1}{2^2} - \frac{1}{\infty^2} \right) \]
Since \( \frac{1}{\infty^2} = 0 \), we have:
\[ \bar{\nu} = R \left( \frac{1}{4} \right) \]

### Step 4: Substitute the value of the Rydberg constant
Given that the Rydberg constant \( R = 10^7 \, \text{m}^{-1} \):
\[ \bar{\nu} = 10^7 \left( \frac{1}{4} \right) = \frac{10^7}{4} \, \text{m}^{-1} \]

### Step 5: Calculate the wave number
Calculating \( \frac{10^7}{4} \):
\[ \bar{\nu} = 2.5 \times 10^6 \, \text{m}^{-1} = 0.25 \times 10^7 \, \text{m}^{-1} \]

### Conclusion
Thus, the wave number of the last line of the Balmer series in the hydrogen spectrum is:
\[ \bar{\nu} = 0.25 \times 10^7 \, \text{m}^{-1} \]

### Final Answer
The correct option is \( 0.25 \times 10^7 \, \text{m}^{-1} \).

---