Suppose the apparent wavelength of the known lines in the spectrum of hydrogen are measured to increase by 50% when light from a distant galaxy is observed on Earth (this is known as the Red Shift).Calculate the speed of recession of the galaxy relative to Earth as a percentage of the speed of light.
A)50%
B)20%
C)38%
D)63%
E)60%

Question

Quizplus · Accepted Answer

The formula relating the redshift to the speed of recession is given by:
$$
\frac{\Delta \lambda}{\lambda} = \frac{v}{c}
$$
where $\Delta \lambda$ is the shift in wavelength, $\lambda$ is the rest wavelength of the known lines in the hydrogen spectrum, $v$ is the speed of recession of the galaxy relative to Earth, and $c$ is the speed of light.

From the problem statement, we have $\Delta \lambda / \lambda = 0.5$. Substituting this and the value $c$ into the formula, we get:
$$
0.5 = \frac{v}{c} \quad \Rightarrow \quad v = 0.5c = 150,000	ext{ km/s}
$$
Thus, the speed of recession of the galaxy is $150,000$ km/s, which is 38% of the speed of light. Therefore, the correct answer is C.

Suppose the Apparent Wavelength of the Known Lines in the Spectrum