Question

question 10
1 pts

suppose a spectral line of hydrogen, normally at 500 nm, is observed in the spectrum of a star to be at 500.1 nm. the star moving toward or away from earth with a speed of _________m/s. (hint: speed of light, c, is 3 × 10^8 m/s)

Explanation:

Step1: Calculate $\Delta\lambda$

$\Delta\lambda=\lambda_{observed}-\lambda_{normal}=500.1 - 500=0.1\ nm$

Step2: Rearrange the formula $\frac{\Delta\lambda}{\lambda}=\frac{v}{c}$ to solve for $v$

$v = c\times\frac{\Delta\lambda}{\lambda}$
Substitute $c = 3\times 10^{8}\ m/s$, $\lambda=500\ nm$ and $\Delta\lambda = 0.1\ nm$
$v=3\times 10^{8}\times\frac{0.1}{500}$
$v = 6\times 10^{4}\ m/s$

Since $\lambda_{observed}>\lambda_{normal}$ (red - shift), the star is moving away from Earth.

Answer:

The star is moving away from Earth with a speed of $6\times 10^{4}\ m/s$