Question

A quasar consumes 1 solar mass of material per year, converting 15 percent of it directly into energy. What is the quasar's luminosity, in solar units?

Answer 1

`L = 1.478 xx 10^13 L_o.`

Explanation:

Quasars are created as a result of mas being swallowed by the supermassive black hole at the center of an active galactic nucleus. The luminosity of a quasar is the rate at which energy is emitted by the quasar. We are given the rate of `1 M_o. "/ yr"`, and Einstein gave us the formula to convert mass into energy.

`E=mc^2`

Here, `m` is the mass converted and `c` is the speed of light. One solar mass is equal to `1.989 xx 10^30"kg"`. Using the mass conversion formula;

`E = (1.989xx10^30"kg")(3 xx 10^8 "m/s")^2`

`E = 1.790 xx 10^47"J"`

Luminosity is measured in watts, `"W"`, or `"J/s"`, so we need to convert years into seconds.

`1"year" = 365"days" = 8,760 "hours" = 525,600 "minutes"`
`= 31,536,000 "seconds"`

So the luminosity of the quasar is;

`L = (1.790 xx 10^47 "J")/(3.154 xx 10^7 "s") = 5.675 xx 10^39 "W"`

For comparison, the luminosity of the Sun is;

`L_o. = 3.828 xx 10^26 "W"`

Which is about 1 ten-billionth of the luminosity of the quasar.

`L = (5.675 xx 10^39"W")/(3.282 xx 10^26"W")=1.478 xx 10^13 L_o.`