JEE MAIN - Physics (2022 - 26th June Evening Shift - No. 16)
For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :
3 $$\times$$ 108 ms$$-$$1
3 $$\times$$ 1010 ms$$-$$1
3.13 $$\times$$ 105 ms$$-$$1
4.48 $$\times$$ 105 ms$$-$$1
Explanation
$${\lambda _{obs}} = {\lambda _{source}}\sqrt {{{1 + {v \over C}} \over {1 - {v \over C}}}} $$
For $$v < < C$$,
$${{670.7} \over {670}} = 1 + {v \over C}$$
$$ \Rightarrow v = {{0.7} \over {670}} \times 3 \times {10^8}$$ m/s
$$ \Rightarrow v \simeq 3.13 \times {10^5}$$ m/s
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