Question

If the speed of light was half the present value, the energy released in a nuclear reaction decreases by

• A. 100%
• B. 75%
• C. 50%
• D. 25%

Hint:

Energy released in nuclear reaction \(E = mc^2\). If \(c\) becomes \(\frac{c}{2}\), energy becomes \(\frac{1}{4}E\).

Answer 1

The Correct Option is B

The energy released in a nuclear reaction is given by Einstein’s mass-energy equivalence: \[ E = mc^2 \] If the speed of light becomes half, \(c' = \frac{c}{2}\), then: \[ E' = m \left(\frac{c}{2}\right)^2 = \frac{mc^2}{4} \Rightarrow \text{Energy reduces to 25% of original} \] So, energy decreases by: \[ 100% - 25% = 75% \]

Answer 2

Step 1: Recall the relationship between energy and speed of light
Energy released in a nuclear reaction is given by Einstein’s equation:
\[ E = \Delta m \, c^2 \]
where \(\Delta m\) is the mass defect and \(c\) is the speed of light.

Step 2: Analyze the effect of changing speed of light
If the speed of light becomes half, i.e., \(c' = \frac{c}{2}\), then the new energy \(E'\) will be:
\[ E' = \Delta m \, \left(\frac{c}{2}\right)^2 = \Delta m \, \frac{c^2}{4} = \frac{E}{4} \]

Step 3: Calculate the percentage decrease in energy
Energy decreases from \(E\) to \(\frac{E}{4}\), which means it is reduced by:
\[ \text{Decrease} = E - \frac{E}{4} = \frac{3E}{4} \]
Expressed as a percentage:
\[ \frac{3E/4}{E} \times 100 = 75\% \]

Step 4: Final Conclusion
If the speed of light were halved, the energy released in a nuclear reaction would decrease by 75%.