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?

##L = 1.478 xx 10^13 L_o.##

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 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.##