Question

A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed v = 0.972c for a distance of 2.73 km before it decays into an electron, a neutrino, and an antineutrino (− → e− v v).

Answer 1

The question from the student relates to the Physics concept of relativistic effects observed in muons created in the Earth's atmosphere; the distance traveled by a muon measured by an observer on Earth is calculated using its speed and lifetime before decay.

Step-by-step explanation:

The question involves concepts from Physics related to muons, subatomic particles that are created when cosmic rays collide with nuclei in the Earth's atmosphere. A muon can be observed from the Earth's surface to travel at significant fractions of the speed of light (expressed as 0.972c where c is the speed of light) before decaying into other particles. The calculation of the distance a muon travels before decaying, taking into account the speed it travels at and the time from production to decay, involves relativistic principles. In the reference provided, a muon moves at 0.950c and has a lifetime of 7.05 microseconds in the Earth-bound observer's frame, covering a distance of 2.01 kilometers. However, in the muon's frame of reference, the lifetime is shorter at 2.20 microseconds, traveling only 0.627 kilometers. This example illustrates the effects of relativistic time dilation and length contraction.