If velocity of a galaxy relative to earth is `1.2 xx 10^(6)ms^(-2)` then percentage increase in wavelength of light from galaxy as compared to the similar source on earth will be :

Options

A. `0.3 %`
B. `0.4 %`
C. `0.5 %`
D. `0.6 %`

Answer

To solve the problem of determining the percentage increase in wavelength of light from a galaxy relative to a similar source on Earth, we can follow these steps:

### Step 1: Understand the relationship between velocity and wavelength
We use the formula for the change in wavelength due to the Doppler effect:
\[ \frac{\Delta \lambda}{\lambda} = \frac{V}{C} \]
where:
- \(\Delta \lambda\) is the change in wavelength,
- \(\lambda\) is the original wavelength,
- \(V\) is the velocity of the galaxy relative to Earth,
- \(C\) is the speed of light.

### Step 2: Substitute the values into the formula
Given:
- \(V = 1.2 \times 10^6 \, \text{m/s}\)
- \(C = 3 \times 10^8 \, \text{m/s}\)

We can substitute these values into the formula:
\[ \frac{\Delta \lambda}{\lambda} = \frac{1.2 \times 10^6}{3 \times 10^8} \]

### Step 3: Simplify the fraction
To simplify the fraction:
\[ \frac{1.2 \times 10^6}{3 \times 10^8} = \frac{1.2}{3} \times \frac{10^6}{10^8} = 0.4 \times 10^{-2} = 4 \times 10^{-3} \]

### Step 4: Calculate the percentage increase
To find the percentage increase in wavelength, we multiply the result by 100:
\[ \text{Percentage increase} = \left(\frac{\Delta \lambda}{\lambda}\right) \times 100 = 4 \times 10^{-3} \times 100 = 0.4\% \]

### Conclusion
The percentage increase in wavelength of light from the galaxy compared to a similar source on Earth is:
\[ \text{0.4\%} \]

### Final Answer
Thus, the correct option is **0.4%**.

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