Question

If $1\, g$ of hydrogen is converted into $0.993\, g$ of Helium, in the thermo nuclear reaction, the Energy released in the reaction is:

• A. $ 63\times {{10}^{20}}\,J $
• B. $ 63\times {{10}^{14}}\,J $
• C. $ 63\times {{10}^{10}}\,J $
• D. $ 63\times {{10}^{7}}\,J $

Answer 1

Answer: (C)

Einstein's mass-energy relation gives the conversion of mass into energy.
If a substance loses an amount $\Delta m$ of its mass, an Equivalent amount $\Delta E$ of energy is produced.
$\Delta E=(\Delta m) c^{2}$
Where $c$ is speed of light.
This is Einstein's mass energy relation.
Given, $ m_{1}=1 g=1 \times 10^{-3} \,kg $
$m_{2}=0.993\, g=0.993 \times 10^{-3} \,kg$
$\therefore \Delta m=m_{1}-m_{2}=\left(1 \times 10^{-3}\right)-\left(0.993 \times 10^{-3}\right) $
$=0.007 \times 10^{-3} $
$=7 \times 10^{-6} \,kg $
$E=7 \times 10^{-6} \times\left(3 \times 10^{8}\right)^{2} $
$E=63 \times 10^{10} \,J$