Question

Particles called π-mesons are produced by accelerator beams. If these particles travel at 2.70×10^8 m/s and live 2.60×10^−8 s when at rest relative to an observer, how long do they live as viewed in the laboratory?

a) 1.75×10^(-8) s
b) 2.88×10^(-8) s
c) 3.85×10^(-8) s
d) 5.42×10^(-8) s

Answer 1

The particle lives approximately 2.88 × 10^-8 seconds as viewed in the laboratory.

Step-by-step explanation:

The time dilation formula is used to calculate the time experienced by an observer in a moving reference frame. The formula is given by:

t' = t / √(1 - v^2/c^2)

where t' is the time observed in the laboratory, t is the time measured by the observer at rest relative to the particle, v is the velocity of the particle, and c is the speed of light. Plugging in the given values, we can calculate the time the particle lives in the laboratory:

t' = (2.60 × 10^-8 s) / √(1 - (2.70 × 10^8 m/s)^2 / (3.00 × 10^8 m/s)^2) ≈ 2.88 × 10^-8 s

Therefore, the particle lives approximately 2.88 × 10^-8 seconds as viewed in the laboratory. The correct answer is option b).