On the basis of the distance to the Coma Cluster of galaxies (90 Mpc) and the Hubble relation, using for the Hubble constant H₀ the value 73 km/sec per million pc, what would be the approximate wavelength shift of the Balmer H $\alpha$ spectral line at 656.3 nm emitted by a galaxy in the cluster because of the general expansion of the universe? (See Box 23-2, Universe, 11th ed.)

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Quizplus · Accepted Answer

The redshift $ z $ can be calculated using the formula $ z = \frac{v}{c} $, where $ v = H_0 \times d $. For $ H_0 = 73 $ km/s/Mpc and $ d = 90 $ Mpc, $ v = 6570 $ km/s. The redshift $ z = \frac{6570}{300,000} \approx 0.0219 $. The wavelength shift $ \Delta \lambda = z \times \lambda_0 = 0.0219 \times 656.3 $ nm, which is approximately 14.4 nm.

On the Basis of the Distance to the Coma Cluster α\alphaα

On the Basis of the Distance to the Coma Cluster $\alpha$