Question

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 it travel if time dilation did not occur? Give the answer to part (c) to two significant figures.

Answer #1

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,...

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...

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 muon is an unstable particle whose mean lifetime is 2.2 ∙
10-6 s as measured by an observer at rest relative to
the muon. A large burst of such muons is produced 6.0 km above the
ground level, after which the muons move towards the surface of the
Earth with a velocity 0.92?. a) What is the mean lifetime of the
muons to a stationary observer on the surface of the Earth? b) What
percentage of the muons reach...

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...

An unstable high-energy particle is created in the laboratory,
and it moves at a speed of 0.989c. Relative to a stationary
reference frame fixed to the laboratory, the particle travels a
distance of 3.16 × 10-3 m before disintegrating. What is (a) the
proper distance and (b) the distance measured by a hypothetical
person traveling with the particle? Determine the particle's (c)
proper lifetime and (d) its dilated lifetime.

A muon is a negatively-charged unstable elementary particle with
a mass equal to 208 times that of the electron, and a charge equal
to that of the electron. Although unstable, the muon does have a
lifetime long enough for it to form a short-lived (muonic) atom, in
which it plays the same role as an electron in an ordinary
atom.
Suppose that a muon forms a muonic atom with a nucleus with
(Z=13) and all electrons have been stripped from...

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...

An unstable high-energy particle is created in the laboratory,
and it moves at a speed of 0.993c. Relative to a stationary
reference frame fixed to the laboratory, the particle travels a
distance of 1.64 × 10-3 m before disintegrating. What is (a) the
proper distance and (b) the distance measured by a hypothetical
person traveling with the particle? Determine the particle's (c)
proper lifetime and (d) its dilated lifetime. Limit your answer to
3 significant digits.

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...

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