Question

Assuming total mass of a star is ~ 1× 1033 kilogram (kg). About 0.1% of the star’s total mass will be used to make the nuclear reaction in the core to provide the energy for the star. The total energy corresponding to the mass of nuclear reaction can be computed by Einstein massenergy relationship E = mc2, where E is energy, m is mass, and c is light speed (c = 3 × 108 meters/second). Assuming the solar power (luminosity) of the star is 9 × 1025 W, which does not change during the lifetime of the star. Please estimate the total lifetime of the star (i.e., the time running out the total energy generated from nuclear reaction by the luminosity).

(A) ~ 1× 1020 seconds

(B) ~ 1× 1021 seconds

(C) ~ 9× 1021 seconds

(D) ~ 1× 1022 seconds

Answer 1

The correct answer is option B.

Step-by-step explanation:

Einstein mass energy relationship

`E = mc^2`

Given mass of star = M =
`1* 10^(33) kg`

Mass of star used to make nuclear energy = m=0.1% of M

`m=(0.1)/(100)* 1* 10^(33)=10^(30) kg`

Speed of light = c =
`3* 10^8 m/s`

Nuclear energy generated = E

`E=mc^2=10^(30) kg* (3* 10^8 m/s)=9* 10^(46) J`

Solar power of the Star,P =
`9\time 10^(25) Watts`

Total life time of the star = T

`Power=(Energy)/(Time)`

`Time =(Energy)/(Power)`

`T=(9* 10^(46) J)/(9\time 10^(25) Watts)`

`T=1* 10^(21) seconds`

Total life time of the star is
`1* 10^(21) years`.