# In one of the galaxies (the distance to the galaxy is 100 Mpc, the Hubble constant is 75 km / sec / Mpc), a supernova breaks out.

In one of the galaxies (the distance to the galaxy is 100 Mpc, the Hubble constant is 75 km / sec / Mpc), a supernova breaks out. a) Estimate at what wavelength you should look for the hydrogen line Ha (laboratory wavelength 6563A) in its spectrum. b) Estimate the width of the line Ha.

In the case of supernova observations, the displacement of lines in its spectrum is caused by two reasons: 1 – expansion of the Universe (displacement of lines to the long-wave region), 2 – expansion of the discarded shell (into the short-wave region if the shell is opaque and splitting of lines if the shell is transparent). The expansion speed of the supernova envelope is ~ 8000 km / sec. Those. the displacement Hα will be equal to Δλ = Vob / s * λ0 = 8000/300000 * 6563 = 175 A towards the blue side (we assume the shell is opaque).
Due to the expansion of the Universe, the displacement will be equal to Δλ = VHubble / c * λ0 = H * R / c * λ = 7500 / s * λ = 7500/300000 * 6563 = 164 A towards the red side.
Those. there is practically no overall displacement, which means that the line must be looked for in the usual place.
The broadening of the line will be mainly caused by the general expansion of the envelope at a speed of 8000 km / s, i.e. the line width will be ~ 200 A.

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