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Question

The time it takes for a black hole to evaporate through the process

of Hawking radiation can be calculated using the following formula, in which M
M is the mass of the black hole in kilograms and t
t is the lifetime of the black hole in seconds:
t=10240×π2 × (G2M3/hc4)
(h=6.63 × 10-34 × (kg ×m2 /s)
(G=6.67 × 10-11 × (m3/kg×s2)
Some scientists speculate that in the far distant future, the universe will consist only of gigantic black holes and scattered subatomic particles. The largest black holes that conceivably might form would have a mass of about a trillion (1012) Suns


a. Use the formula to calculate the lifetime of such a giant black hole. (Hint: Your calculator may not be able to handle the large numbers involved in this problem, in which case you will need to rearrange the numbers so that you can calculate the powers of 10 without your calculator.)
tblack hole = ? years


b.How does your answer compare to the current age of the universe? Assume the current age of the universe is about 1010 years.
tblack hole/tuniverse = ?

Step-by-step answer

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