Radioactive particles moving at 0.80 c are measured to have a half-life of 4.3 × 10^-8 s. What is their half-life when at rest? A) 7.2 × 10^-8 s B) 2.6 × 10^-8 s C) 3.4 × 10^-8 s D) 1.6 × 10^-8 s E) 1.7 × 10^-7 s

Question

Quizplus · Accepted Answer

The half-life of the radioactive particles as they move at 0.80 c is given by:
t' = t/(gamma)
where t is the half-life at rest and gamma is the Lorentz factor given by:
gamma = 1/sqrt(1 - v^2/c^2) = 1/sqrt(1 - 0.8^2) ≈ 1.67

Plugging in the values given, we have:
4.3 × 10^-8 s = t/(1.67)
t ≈ 7.2 × 10^-8 s

Therefore, the half-life when at rest is approximately:
t ≈ 7.2 × 10^-8 s / 1.67 ≈ 2.6 × 10^-8 s

The best choice is B.

Radioactive Particles Moving at 0