Question

A muon is a type of unstable subatomic particle. When high-speed particles from outer space (sometimes called "cosmic rays") collide with atoms in the upper atmosphere, they can create muons which travel toward the Earth. Suppose a muon created in the atmosphere travels at a speed of 0.941c toward the Earth's surface for a distance of 3.48 km, as measured by a stationary observer on Earth, before decaying into other particles.

(a) As measured by the stationary observer on Earth, how much time elapses (in s) between the muon's formation until its decay?

(b) Find the value of the gamma factor that corresponds to the muon's speed.

(c) Now imagine an observer that "rides along" with the traveling muon, moving at the same speed. From this observer's perspective, how much time elapses (in s) between the muon's formation until its decay?

(d) Again from the perspective of the observer traveling along with the muon, what distance (in m) does the muon travel, from its formation to its decay? (e) Now imagine a third observer, who is traveling toward the muon at a speed of c/2, as measured with respect to the Earth. How does the muon's lifetime, as measured by this observer, compare to the lifetime as measured by the stationary observer on Earth?

The lifetime measured by the moving observer is the same as the lifetime measured by the observer on Earth.
The lifetime measured by the moving observer is longer than the lifetime measured by the observer on Earth.
The lifetime measured by the moving observer is shorter than the lifetime measured by the observer on Earth.
Not enough information is known to make a comparison.

Answer 1

(a) The velocity is given and the distance the muon covers before decaying is also given. Therefore the time period when muon is stable is.

(b) The gamma factor is given by,

(c) From the muon's reference frame we can say that the time will be, (there will be time dilation)

(d) From the perspective of the observer in muon's reference frame the distance travelled will be, (The distance will be shorter due to Length contraction),