If the average quasar has a luminosity of 10¹⁴ L_⨀ and an absolute magnitude of −30,and you discover one that has an apparent magnitude of +10,then what is its distance? A)10,000 Mpc B)5,000 Mpc C)1,000 Mpc D)500 Mpc E)0.1 Mpc

Question

Quizplus · Accepted Answer

We can use the distance modulus formula:

m - M = 5 log(d/10)

where m is the apparent magnitude, M is the absolute magnitude, and d is the distance in parsecs.

First, we need to convert the luminosity of the average quasar in the question to an absolute magnitude:

L = 10^44.114 erg/s

M = -2.5 log(L/Lsun) - 26.74

M = -2.5 log(10^44.114/3.846×10^33) - 26.74

M = -30.0

So, the absolute magnitude of the discovered quasar is:

m - M = 40

m = -30 + 40 = 10

Now we can use the distance modulus formula to solve for the distance:

10 - (-30) = 5 log(d/10)

40 = 5 log(d/10)

log(d/10) = 8

d/10 = 10^8

d = 10^9 pc

1 Mpc = 10^6 pc

d = 10^3 Mpc

Therefore, the answer is C) 1,000 Mpc.

If the Average Quasar Has a Luminosity of 1014 L⨀

If the Average Quasar Has a Luminosity of 10¹⁴ L_⨀