Question

Muons are unstable subatomic particles that decay to electrons with a mean life-time of 2.3μs. They are produced when cosmic rays bombard the upper atmosphere about 12 km above the earth's surface, and they travel very close to the speed of light c=3.00 ×108 m/s. The problem we want to address is why we see any of them at the earth's surface. What is the greatest distance a muon could travel during its 2.3- s lifetime?

Answer 1

Firstly, we need to understand the values given and what they represent. We are given the speed of light, which is approximately 3.00 x 10^8 meters per second. We also have the mean lifetime of a muon, which is 2.3 x 10^-6 seconds.

The problem asks for the greatest distance a muon could travel during its lifetime. Since speed is distance over time, we can rearrange this formula to find the distance by multiplying speed by time.

First, we take the speed of light which is 3.00 x 10^8 m/s.

Then we multiply this by the mean lifetime of a muon which is 2.3 x 10^-6 seconds.

This calculation shows us how far light can travel in the span of the mean lifetime of a muon.

Finally, by carrying out this multiplication, we find that the maximum distance a muon can travel in its lifetime is approximately 690 meters.