Question

In a nuclear fusion reaction mass defect is 0.2%. What will be amount of energy released in the fusion of 1 kg mass?

Hint:

Use \( E = \Delta m\, c^2 \) with \( \Delta m = 0.2\% \) of 1 kg, i.e. \( 2 \times 10^{-3} \) kg.

Answer 1

Step 1 (Concept): In a nuclear reaction the mass that disappears (the mass defect \( \Delta m \)) is converted into energy according to Einstein's mass-energy relation \( E = \Delta m\, c^2 \).

Step 2 (Find the mass defect): Mass defect is 0.2% of the reacting mass.
\[ \Delta m = \frac{0.2}{100} \times 1\ \text{kg} = 2 \times 10^{-3}\ \text{kg} \]

Step 3 (Substitute in \( E = \Delta m c^2 \)): with \( c = 3 \times 10^{8}\ \text{m/s} \),
\[ E = (2 \times 10^{-3}) \times (3 \times 10^{8})^2 \]

Step 4 (Arithmetic):
\[ E = (2 \times 10^{-3}) \times (9 \times 10^{16}) = 18 \times 10^{13} \]
\[\boxed{E = 1.8 \times 10^{14}\ \text{J}}\]