Question

The \[6563{A^ \circ }{H_\alpha }\] line emitted by hydrogen in a star is found to be red-shifted by \[15{A^ \circ }\].The speed with which the star is receding from earth is
A. \[3.2 \times {10^5}m{s^{ - 1}}\]
B. \[6.87 \times {10^5}m{s^{ - 1}}\]
C. \[2 \times {10^5}m{s^{ - 1}}\]
D. \[12.74 \times {10^5}m{s^{ - 1}}\]

Answer 1

Hint: To solve this question, we have to know about light rays and shifting of lights. Astronomers can notice light from distant universes. The dark lines in the spectra from inaccessible universes shows an expansion in frequency. The lines are moved or moved towards the red finish of the range. This impact is called red shift. The outline shows part of the emanation range of light from a removed world.

Complete step by step answer:
Here according to the question we know that, the wavelength of \[{H_\alpha }\] line, \[\lambda = \]\[6563{A^ \circ }\]
\[\Rightarrow \lambda = 6563 \times {10^{ - 10}}\]
We know that, redshift observed in star \[(\lambda ' - \lambda ) = 15{A^ \circ } = 15 \times {10^{ - 10}}\]
Let the velocity of the star with which it is receding away from the earth be v. We know that, redshift relation is, \[(\lambda ' - \lambda ) = \dfrac{v}{c}\lambda \]
\[v = (\lambda ' - \lambda )\dfrac{c}{\lambda }\]
\[Rightarrow v = \dfrac{{3 \times {{10}^8} \times 15 \times {{10}^{ - 10}}}}{{6563 \times {{10}^{ - 10}}}}\]
\[\therefore v = 6.87 \times {10^{ - 5}}m{s^{ - 1}}\]

So, here the right answer is \[v = 6.87 \times {10^{ - 5}}m{s^{ - 1}}\] which is the option B.

Note: We know that, The Doppler impact says that frequency increments as items move away from us, so light that is red moved should have a light source moving endlessly from us. So, Showing up here is a chart of a star moving endlessly from us, which makes the frequency of light increment, making more red light. We have to keep this in our mind so that we can solve these kinds of problems easily. We know that, In material science, redshift is where electromagnetic radiation, (for example, light) from an item goes through an expansion in frequency. Space itself is growing, making objects become isolated without changing their situations in space.