Question

A star emitting a wavelength of $6000\mathring{\text{A}}$ is moving away from the earth with a speed of $5\text{km/s}$. Due to Doppler effect, the change in wavelength will be,
(Given: $c=3\times {10}^8\text{m/s}$)

• A. $0.1\mathring{\text{A}}$
• B. $0.05\mathring{\text{A}}$
• C. $0.2\mathring{\text{A}}$
• D. $1\mathring{\text{A}}$

Answer 1

The correct option is A $0.1\mathring{\text{A}}$

The Doppler shift in wavelength is given by,

$\frac{\Delta \lambda }{\lambda }=\frac{v_r}{c}\Rightarrow \Delta \lambda =\lambda \times \frac{v_r}{c}$

Here,
$\lambda =6\times {10}^{-7}\text{m},c=3\times {10}^8\text{m/s}$
$v_r=5000\text{m/s}$

$\Delta \lambda =\frac{5000}{3\times {10}^8}\times 6\times {10}^{-7}=1\times {10}^{-11}\text{m}$

$\therefore \Delta \lambda =0.1\mathring{\text{A}}$

Hence, $\left(A\right)$ is the correct answer.