Question

A subatomic particle with an average lifetime of 2.1x10^(-9)s at rest is placed into a particle accelerator, and is made to move at 2.6x10^(8) m/s. Calculate the average lifetime of the particle in the accelerator.

Answer 1

Answer on Question 64275, Physics, Quantum Mechanics

Question:

A subatomic particle with an average lifetime of $2.1 \cdot 10^{-9} \, s$ at rest is placed into a particle accelerator, and is made to move at $2.6 \cdot 10^{8} \, m/s$. Calculate the average lifetime of the particle in the accelerator.

Solution:

We can find the average lifetime of the particle in the accelerator from the time dilation formula:

$$\Delta t' = \frac{\Delta t}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{2.1 \cdot 10^{-9} \, s}{\sqrt{1 - \frac{\left(2.6 \cdot 10^{8} \, \frac{m}{s}\right)^{2}}{\left(3.0 \cdot 10^{8} \, \frac{m}{s}\right)^{2}}}} = 4.2 \cdot 10^{-9} \, s.$$

Answer:

$$\Delta t' = 4.2 \cdot 10^{-9} \, s.$$

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