Question

A star is moving towards the earth with a speed of $4.5\times {10}^{6}m/s$. If the true wavelength of a certain line in spectrum received from the star is $5890\mathring{A}$, its apparent wavelength will be about [ $c=3\times {10}^{8}m/s$]

• A. $5890\mathring{A}$
• B. $5978\mathring{A}$
• C. $5802\mathring{A}$
• D. $5896\mathring{A}$

Answer 1

Answer: (C)

$5802\mathring{A}$

We know that the apparent wavelength is given as:

${\lambda }^{\prime }=\lambda (1-\frac{v}{c})$

${\lambda }^{\prime }=5890(1-\frac{4.5\times {10}^6}{3\times {10}^8})$

$\approx 5802\stackrel{o}{A}$