The sun radiates at a power of 3.9 $\times$ 10²⁶ W.How long does it take for the sun to lose an amount of mass equal to the mass of the Earth (6.0 $\times$ 10²⁴ kg)? Choose the first answer that is correct. A) less than one year B) less than 1000 years C) less than 10⁶ years D) less than 10⁸ years E) more than 10⁸ years

Question

Quizplus · Accepted Answer

We can use the Einstein's famous equation E=mc² to find the mass-energy equivalence. The energy radiated by Sun is given as 3.9×10^26 W. We can find the mass equivalent using E=mc². So, 
3.9×10^26 = m(c²)
m = 3.9×10^26 / (9×10^16) = 4.33×10^9 kg/s
This means the Sun is losing 4.33×10^9 kg of mass every second. 
To find how much time it would take for the Sun to lose mass equal to the Earth's mass, we divide the mass of the Earth by the mass loss per second rate of the Sun.
time = (mass of Earth) / (mass loss per second rate of Sun)
time = 6×10^24 / (4.33×10^9)
time = 1.39×10^15 s
This is less than 10^18 years, but still much greater than 10^18 seconds. Therefore, the answer is D, less than 10^18 years.

The Sun Radiates at a Power of 3 ×\times× 1026 W ×\times×

The Sun Radiates at a Power of 3 $\times$ 10²⁶ W $\times$