The Hercules Cluster of galaxies shown in Figure 23-18 (Universe, 11th ed.) is at a distance of 650 million ly from our galaxy. Using a Hubble constant of 23 (km/s)/Mly, at what wavelength will the Balmer H $\alpha$ spectral line, with rest wavelength = 656.3 nm, be seen in the spectrum of a galaxy in this cluster?

Question

Quizplus · Accepted Answer

The formula to use here is:

observed wavelength = rest wavelength × (1 + z)

Where z is the redshift, given by:

z = H × d

Where d is the distance to the galaxy in Mly.

Plugging in the values given:

z = 23 × 650 = 14950 km/s
d = 650 Mly = 650 × 10^6 × 9.461 × 10^12 km = 6.1463 × 10^18 km

So:

z = 0.0498
observed wavelength = 656.3 nm × 1.0498 = 689.0 nm

Therefore, the correct answer is B.

The Hercules Cluster of Galaxies Shown in Figure 23-18 (Universe α\alphaα

The Hercules Cluster of Galaxies Shown in Figure 23-18 (Universe $\alpha$