The galaxy with a hydrogen beta absorption of 496 nm then the galaxy's distance from us in mega-light years (mly) will be equal to 277.54 Mly.
The distance between two identical locations (adjacent crests) in successive cycles is known as the wavelength, and it is used to describe waveform signals that are transmitted over wires or into space. Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimeters (mm).
As per the given information in the question,
The line's hydrogen laboratory wavelength, λ = 486.1 nm
The galaxy's spectrum's wavelength, λ' = 496.0 nm
Then, the change in wavelength,
Δλ = λ' - λ
Δλ = 9.9 nm
The speed of light, c = 2.998 × 10⁵ km/s
Use the equation of Doppler's effect,
v = c × Δλ/λ
v = 6,105.75 km/s
So, the radial velocity will be 6105.78 km/s.
v = H₀d
Here, v is the velocity of the galaxy, d is the distance between galaxies and H₀ is Hubble's constant.
d = v/H₀
d = 6105.75/22
d = 277.54 Mly
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