The spectral line for a given element in the light received from a distant star is shifted towards longer wavelength side by `0.025%`. Calculate the velocity of star in the line of sight.

Options

A. `7.5xx10^(4)ms^(-1)`
B. `-7.5xx10^(4)ms^(-1)`
C. `3.7xx10^(4)ms^(-1)`
D. `-3.7xx10^(4)ms^(-1)`

Explanation

To solve the problem of determining the velocity of the star in the line of sight based on the redshift of a spectral line, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Redshift**: The problem states that the spectral line is shifted towards longer wavelengths by 0.025%. A shift towards longer wavelengths indicates a redshift, which means the star is moving away from us.

2. **Expressing the Redshift**: The redshift \( z \) can be expressed in terms of the change in wavelength \( \Delta \lambda \) and the original wavelength \( \lambda \):
\[ z = \frac{\Delta \lambda}{\lambda} \]
Given that the shift is 0.025%, we can express this as:
\[ z = \frac{0.025}{100} = 0.00025 \]

3. **Relating Redshift to Velocity**: The velocity \( V \) of the star can be calculated using the formula:
\[ V = z \cdot c \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \) m/s.

4. **Calculating the Velocity**: Substituting the value of \( z \) into the equation:
\[ V = 0.00025 \cdot (3 \times 10^8 \text{ m/s}) \]

5. **Performing the Calculation**:
\[ V = 0.00025 \times 3 \times 10^8 = 0.00075 \times 10^8 = 7.5 \times 10^4 \text{ m/s} \]

6. **Interpreting the Result**: Since this is a redshift, the velocity will be negative, indicating that the star is moving away from us:
\[ V = -7.5 \times 10^4 \text{ m/s} \]

### Final Answer:
The velocity of the star in the line of sight is approximately \( -7.5 \times 10^4 \) m/s.

---