A star similar to our sun radiates energy at the prodigious rate of 4.8 x 10^26  Assuming that the star has radiated at this same rate for its entire lifetime of 4.2 x 10^9 y, and that its current mass is 2.1 x 10^30 kg, what percentage of its original mass has been converted to energy?

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In order to determine the percentage of the star's original mass that has been lost to radiation we must find the original mass of the star.  You do not give any units for the radiation rate but I am assuming its J/year, or Joules per year.  If we multiply the life of the star by the radiation rate we get 4.8 x 10^26 J/year * 4.2 x 10^9 years = 2.016 x 10^36 Joules.  Now we must conver this energy into mass.  We can do this with Einstein's classic equation E=mc^2.

2.016 x 10^36 J = m(299792458 m/s)^2

m = 2.24 x 10^19 kg

This is the mass of the star that has been lost to radiation over its lifetime.  If we add this to the current mass of the star we get:

2.24 x 10^19 kg + 2.1 x 10^30 kg = 2.1000000000224 x 10^30 kg

This is the original mass of the star.  We now divide the mass of the star lost to radiation by the original mass of the star to get the percent loss:

2.24 x 10^19 kg/2.1000000000224 x 10^30 kg * 100 = 1.07 x 10^-9 %

The star has lost 1.07 x 10^-9% of its mass to energy.

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