Question

Suppose that the sun consists of the energy of hydrogen atom and releases the energy by the nuclear reaction, $4_1^{1}H{\to }_2^4$He with 26 MeV of energy released. If the total output power of the sun is assumed to remain constant at $3.9\times {10}^{26}$W, the time it will take to burn all the hydrogen is:

(Take the mass of the sun as $1.7\times {10}^{30}$kg)

• A. $8/3\times {10}^{18}sec$
• B. $9/3\times {10}^{18}sec$
• C. $7/2\times {10}^{18}sec$
• D. $5/3\times {10}^{18}sec$

Answer 1

The correct option is A $8/3\times {10}^{18}sec$

Mass of sun $=1.7\times {10}^{30}kg=1.7\times {10}^{33}g$

Total energy produced during burning of all the hydrogen of sun is,

$\frac{1.7\times {10}^{33}\times 6.023\times {10}^{23}}{4}\times 26\times {10}^6=6.66\times {10}^{63}eV$,

$\because$ one nuclear reaction consumes 4 $H$ atoms and releases 26 MeV of energy.

As, $6.66\times {10}^{63}eV=1.07\times {10}^{45}Ws$

The total output power of the sun is $3.9\times {10}^{26}W$.

The time it will take to burn all the hydrogen is $\frac{1.07\times {10}^{45}Ws}{3.9\times {10}^{26}W}=8/3\times {10}^{18}sec$.