Question

An astronomer observes a hydrogen line in the spectrum of a star. The wavelength of hydrogen in the laboratory is 6.563 x 10-7m, but the wavelength in the star's light is measured at 6.56186 x 10-7m. Which of the following explains this discrepancy? A.The star is moving away from Earth B. The wavelength of light that the star is emitting changes constantly. C.The frequency of light that the star is emitting changes constantly. D. The star is approaching Earth.

Answer 1

Answer:

D. The star is approaching Earth.

Explanation:

As we know by the doppler's effect of light that

$\frac{\Delta \nu}{\nu} = \frac{v}{c}$

here we know that

$\Delta \nu$ = change in frequency

here we know that the wavelength of light coming from the star is decreased so the frequency will increase

$\Delta \nu = \frac{c}{\lambda'} - \frac{c}{\lambda}$

$\Delta \nu =(3\times 10^8)(\frac{1}{6.56186 \times 10^{-7}} - \frac{1}{6.563 \times 10^{-7}})$

$\Delta \nu = 7.9414 \times 10^{10} Hz$

now we have

$\frac{7.9414 \times 10^{10}}{\nu} = \frac{v}{c}$

here we know that

$\nu = \frac{3\times 10^8}{6.563 \times 10^{-7}} = 4.57 \times 10^{14} Hz$

now we have

$v = 5.2 \times 10^4 m/s$

So here correct answer is

D. The star is approaching Earth.