In a fission process, the decrease in mass is 0.01%. How much energy could be obtained from the fission of 0.1g of the material
A
\( 9.0 \times 10^{9}J \)
B
\( 9.0 \times 10^{10}J \)
C
\( 6.3 \times 10^{11}J \)
D
\( 9.0 \times 10^{11}J \)
Verified Correct Answer: A.
Physical Principles & Numerical Solution
In general, the energy released during nuclear fission is given by Einstein's mass-energy equation, given by
\( E = \Delta MC^2 \)
Where \( \Delta m\) is the mass defect, and C is the speed of light.
Therefore
\( \Delta m = 0.01% \text{of} 1.0g = \frac{0.01}{100}\times 1.0g \)
= 1.0 \(\times 10^{-4} \)
= 1.0 \(\times 10^{-7}kg\)
\(\text{Energy Released } = \Delta MC^2 \)
= 1.0 \(\times 10^{-7} \times (3.0 \times 10^8)^2\)
= 1.0 \(\times 10^{-7} \times 9.0 \times 10^{16} \)
= 9.0 \(\times 10^9 J \)
Source: Official Exam / Past Question Archive