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),

Muons are unstable subatomic particles that decay with a mean
lifetime of 2.197us
(producing electrons and neutrinos) as measured in the inertial
frame of the muons. Many
are produced in the upper atmosphere about 10 km above the surface
of the Earth, and
some of them travel very near the speed of light on their way to
the surface.
A) Calculate the largest distance any particle can travel in
2.197us, with both the time
and the distance measured by observers...

Muons are unstable subatomic particles that decay to electrons
with a mean lifetime of 2.2 μs . They are produced when cosmic rays
bombard the upper atmosphere about 11.1 km above the earth's
surface, and they travel very close to the speed of light. The
problem we want to address is why we see any of them at the earth's
surface.
A. What is the greatest distance a muon could travel during its
2.2 μs lifetime?
B. According to your...

A muon formed high in Earth's atmosphere travels towards Earth
at a speed
v = 0.970c
for a distance of 4.30 km as measured by an observer at rest
with respect to Earth. It then decays into an electron, a neutrino,
and an antineutrino.
(a) How long does the muon survive according to an observer at
rest on Earth?
(b) Compute the gamma factor associated with the muon.
(c) How much time passes according to an observer traveling with
the...

One of the many fundamental particles in nature is the muon
mu. This particle acts very much like a "heavy electron." It has a
mass of 106 MeV/c^2, compared to the electron's mass of just 0.511
MeV/c^2. (We are using E = mc^2 to obtain the mass in units of
energy and the speed of light c).
Unlike the electron, though, the muon has a finite lifetime,
after which it decays into an electron and two very light particles
called...

A pion is an unstable particle which decays into a muon (which
is also unstable and further decays into an electron). The pion’s
average lifetime when it is at rest is 26 ns. If the pion moves
with a speed of 0.9819 c, what is (a) its average lifetime (ns) as
measured by an observer on Earth and (b) the average distance (m)
it travels before decaying as measured by an observer on Earth? (c)
What average distance (m) would...

Muons are elementary particles with a small mass. They are often
created in the atmosphere by cosmic ray collisions. Once the muon
is created, its lifetime is only 2 microseconds (2×10−6 seconds). A
typical velocity is 0.9999 c, just 0.1 % below the speed of light.
Without relativity, the muons would only travel 600 meters before
decaying, yet we see muons created 10 km in the air reach our
instruments on the ground.
a) Consider a muon created 10km above...

6. The muon particle was a bit of a strange case until
relativity came along. The muon forms 1.0 × 104m above the surface
of the Earth and speeds downwards at 0.998c. From the particle’s
perspective, it has a lifetime of 2.2 × 10−6 s.
a) Use classical physics to determine how far the muon should be
able to travel in its lifetime.
b) This travel distance was puzzling since the muon was observed
in great numbers at Earth’s surface....

A ?+ is a subatomic particle called a Pion that is positively
charged. It has a mean lifetime of about 26 ns (26x10-9 s) as
measured in the pion's frame of reference. Suppose a pion is
created in the atmosphere and is moving at 0.856c relative to a
stationary observer on Earth. How far in meters does the pion
travel during its lifetime according to the Earth-bound observer?
Assume 3 significant figures.
The formula d=speed x time DOES NOT WORK...

A lab worker is watching a bunch of particles zing through her
particle accelerator. She observes one particle that's moving at
61% of the speed of light for its whole life, and she sees that it
travels a certain distance before decaying.
How fast would a second particle need to be traveling for its
entire life if the lab worker is to see this second particle travel
twice as far as the first? Assume all particles in this problem
would...

Subatomic particles called pions are created when protons,
accelerated to speeds near the speed of light in a particle
accelerator, smash into the nucleus of the target atom. Charged
pions are unstable particles that decay into muons with a half-life
of 1.8 x 10-8 s. Pions have been
investigated for use in cancer treatment because they pass through
tissue with minimal damage until they decay. As they decay the
release significant energy. The speed of the pions can be adjusted...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 34 minutes ago

asked 35 minutes ago

asked 38 minutes ago

asked 38 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago