Question

The velocity of a particle at which the kinetic energy is equal to its rest energy is

• A. \( \frac{3c}{2} \)
• B. \( \frac{c}{\sqrt{2}} \)
• C. \( \frac{3c}{2} \)
• D. \( \frac{c\sqrt{3}}{2} \)

Hint:

When kinetic energy equals rest energy, use relativistic formulas to find the speed of the particle.

Answer 1

The Correct Option is D

Step 1: Relating kinetic and rest energy.
At the velocity \( v \), the kinetic energy is equal to the rest energy. This gives us the relation \( \frac{1}{2}mv^2 = mc^2 \), leading to \( v = c \sqrt{3}/2 \).
Step 2: Conclusion.
Thus, the velocity at which the kinetic energy equals the rest energy is \( \frac{c\sqrt{3}}{2} \), so the correct answer is option (D).

Final Answer: \[ \boxed{\frac{c\sqrt{3}}{2}} \]