Question

In a nuclear fusion reaction, if the mass defect is 0.25%, then the energy released in the fusion of 400 $\mu$g mass of a substance is

• A. $9\times10^{7}$ J
• B. $9\times10^{10}$ J
• C. $4.5\times10^{7}$ J
• D. $4.5\times10^{10}$ J

Hint:

Use $E = \Delta m c^2$ with $\Delta m$ in kg, $c = 3\times10^8$. Convert $\mu$g to kg ($10^{-9}$ kg). Percentage defect applies to initial mass. Compare with fission/fusion energy yields.

Answer 1

The Correct Option is A

1. Mass defect $\Delta m$ is the mass converted to energy in fusion, given as 0.25% of the initial mass.
2. Initial mass $m = 400 \, \mu$g = $400 \times 10^{-6}$ g = $4 \times 10^{-4}$ g = $4 \times 10^{-7}$ kg.
3. $\Delta m = 0.0025 \times 4 \times 10^{-7} = 10^{-9}$ kg.
4. Energy released $E = \Delta m \, c^2$, where $c = 3 \times 10^8$ m/s.
5. Calculate $c^2 = 9 \times 10^{16}$ m$^2$/s$^2$, so $E = 10^{-9} \times 9 \times 10^{16} = 9 \times 10^7$ J.
6. Therefore, the correct option is (1) $9\times10^{7}$ J.