Question

The wavelength of the red-pink line emitted by a laboratory sample of excited hydrogen is 656 nm. Taking a spectrum of a glowing nebula, you find that the same red-pink line of hydrogen appears at 662 nm. You conclude that the nebula
A. Is 1% hotter than hydrogen in the laboratory sample.

B. Is moving towards us at about 1% the speed of light.

C. Is 1% cooler than hydrogen in the laboratory sample.

D. Is moving away from us at about 1% the speed of light

Answer 1

Answer:

Choice D) The nebula is moving away from the observer.

Explanation:

Is the emission here a result of electron transition or thermal radiation?

• The energy difference between two atomic energy levels is discrete. As a result, emissions due to electron transition exist as discrete lines.
• On the contrary, the thermal radiation of objects above 0 degree Kelvins exists as a continuous frequency spectrum.  

The red-pink emission here is as a line rather than a continuous spectrum. In other words, the red-pink line observed is a result of electron transition. The energy difference will be constant. That should be the same case on the earth as it is in space at the nebula.

Also, this energy difference does not depend on the temperature of the hydrogen. Only that at higher temperature, low-energy radiations will be less prominent. The wavelength will still be 656 nm when the light was emitted from the nebula.

The wavelength observed on the earth is longer than the wavelength emitted. The Doppler's effect is likely to be responsible. As the star moves away from the earth, the distance that light from the star needs to travel keep increasing. Consider two consecutive peaks from the star. When compared with the first peak, the second peak will need to travel a few more kilometers and will need a few more fractions of a second to get to the earth. It would appear to an observer on the earth that the frequency of the light is lower than it actually is. Accordingly, the wavelength will appear to be longer than it was when emitted from the star.

Conversely, the wavelength will appear shorter if the source is moving toward to observer. For this star, the wavelength appears to be longer than it really is. In other words, the star is moving away from the earth.

The ratio between the speed at which the star moves away from the earth and the speed of the light can be found using the equation: (Source: AstronomyOnline)

$\displaystyle \frac{v}{c} = \frac{\Delta \lambda}{\lambda_0} \approx 0.009$.