The hydrogen Balmer H $\alpha$ line with laboratory wavelength 656.3 nm is identified in emission in the spectrum of a quasar at 1968.9 nm. What is its velocity with respect to us?
A)0.8c toward us
B)0.8c away from us
C)1.2c toward us
D)1.2c away from us

Question

Quizplus · Accepted Answer

The observed wavelength is longer than the rest wavelength, indicating the quasar is moving away from us. The redshift $z$ is given by $z = \frac{\lambda_{observed} - \lambda_{rest}}{\lambda_{rest}}$, so $z = \frac{1968.9 - 656.3}{656.3} \approx 2$. The velocity $v$ relative to the speed of light $c$ is given by $v = zc$, for $z \ll 1$, but for $z > 1$, it indicates a significant fraction of the speed of light. Here, $v$ is not directly $zc$ because $z$ is not much less than 1, but we can infer the object is moving away at a high speed. The correct interpretation of redshift for high $z$ values involves relativistic formulas, which would show the quasar moving away at a significant fraction of the speed of light, but none of the given options accurately reflects the exact calculation for such a high $z$. However, the closest correct interpretation based on the options provided and the understanding that the quasar is moving away is option B, 0.8c away from us, acknowledging that the precise velocity calculation would require a more detailed relativistic approach.

The Hydrogen Balmer H α\alphaα Line with Laboratory Wavelength 656

The Hydrogen Balmer H $\alpha$ Line with Laboratory Wavelength 656