The lifetime of a muon is 2.20 ?s. If you measured its mass to be 105.7 MeV/c2, what would be the minimum (Heisenberg) uncertainty in this value? Sketch the situation, defining all of your variables
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The lifetime of a muon is 2.20 ?s. If you measured its mass to be 105.7 MeV/c2, what would be the minimum (Heisenberg) uncertainty in this value?
Sketch the situation, defining all of your variables

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- Please answer all three parts! Thank you. Stanford has a linear particle accelerator (SLAC) which is 3 km long that produces electrons with a total energy of 50 GeV. These electrons lead exciting (albeit brief) lives, zooming along the accelerator before slamming into a target to produce other high-energy particles. a. Consider the viewpoint of one of the electrons. From the electron’s point of view, how long is the accelerator? Note that it is possible to answer this question without calculating the electron’s velocity. b. Let’s figure out how fast the electrons are traveling. Start by solving for β = u/c in terms of 1/γ following the trick we used in class. Use the binomial expansion if that is helpful. At what speed does a 50 GeV electron travel? c. The Large Hadron Collider (LHC) at CERN presently accelerates protons to a total energy of 6.5 TeV. Imagine a pulse of light, a 50 GeV electron, and a 6.5 TeV proton race each other along a 3 km distance. The light pulse will surely win…A beam of π+meson (pions) at Fermilab are traveling at a speed of 0.92cwithrespect to the laboratory. The proper mean lifetime for these pions is 2.6×10−8s.(a) Is this proper lifetime measured in the laboratory frame or the frame of the pions?Why? (b) What is the mean lifetime as measured in the other frame of reference?The Tevatron was a large particle accelerator that would collide beams ofprotons and anti-protons to see what would come out of the collisions.a) Let’s assume that each particle (in both beams) was accelerated to a total energy of100 GeV. What is the speed of the protons (relative to the speed of light) if you assumethe mass of the proton is equal to 1 GeV/c^2? Write your answer in terms of the speed oflight—keep it as a decimal times “c”. You will need several decimal places.b) Suppose that you now accelerate each particle to a speed of 0.9c. Since they are movingin opposite directions, what is the speed that one would measure for the speed of the otherparticle? Just give the absolute value of this speed. Don’t worry about the sign.c) Given your answer in part b, what is the energy of that one particle would measure forthe other particle?
- A particle has a mass of 6.4E-27kg and a momentum of 3.5E-18 kg.m/s. Determine the energy of that particle in GeV (1GeV=1E9 eV). Keep three significant digits.The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 10-8 s. (a) If the meson moves with a speed of 0.94c, what is its mean lifetime as measured by an observer on Earth? (b) What is the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur?MASS OF A PROTON: 1.007825 U; MASS OF A NEUTRON: 1.008665 U 10.. What are the four fundamental Forces (interactions) - Describe their interactions and ranges.
- If you have a positive look (pi+, mass: mpi = 2.50 x 10-28 kg) at rest and it decays to a positive muon (u+, mass: mu = 1.88 x 10-28 kg) and a neutrino. 1. How much gas is released during the decay process in MeV? If the rest mass of a neutrino is assumed to be negligible. 2. Why is the neutrino required for this decay to occur?Name: Hubble Distances Redshift z parameter The relativistic redshift is parametrized by z and given by Δ In terms of the scale factor, 2= X do - de de 1+z= ao a (2) Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which has been observed at a wavelength of 1.64 μm. Astro 001 Fall 2022 Problem 02. How much smaller was the universe when this light was emitted? U₁ = DHO Using the redshift to measure the velocity, we find D~ (1) 0.1 Hubble's Law Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product of the distance and the Hubble constant. (3) ZC Ho where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement of the Hubble constant is Ho = 71 (km/s)/Mpc. Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01? 1 pc = 3.26 ly.A particle's dynamics are considered "relativistic" when its velocity is a significant fraction of the speed of light. For example, the mass of a moving particle seen by a stationary observer increases in proportion to the square root of 1/(1 - (v/c)2). For typical speeds in the everyday world it is not noticeable, but take a fast moving fundamental particle and you may have apparent mass increases or changes in its lifetime as a consequence of time dilation. Look at this factor for the electron you measured at 100 V in the glass globe. Pick the best answer. The effect is less than 0.1 %. The effect is around 1%. The effect is around 10%. The effect is a factor of 2 change in mass.
- In some experiment, we found the fast meson’s velocity is vf=0.9999c while the slow meson’s velocity is vs=0.9955c. Using unit of c in this problem. (leave two decimal places of your result, i.e. like 1.23) (a) Calculate the ratio of the fast meson's lifetime in the laboratory frame to the slow meson's lifetime in the laboratory frame. (b) Calculate the ratio of the fast meson's decay length to the slow meson's decay length.A beam of radioactive particles travels at a speed of 2.5 x 10^8 m/s. The half-life of the particles in the beam is measured to be 1.4μs by an outside observer. Determine the half-life of those particles when they are at rest with respect to the observer. [2 marks] When I performed calculations I considered the time given to be relativistic time as it is measured by an outside observer, however when I look up the answer, they treat the time given as the proper time and not the relatavistic time. Why is that?The neutron has a mass of 1.67 ✕ 10−27 kg. Consider a neutron moving with a speed of 0.960c. (Enter your answer in GeV.) (a) What is its rest energy? GeV (b) What is its total energy? GeV (c) What is its kinetic energy? GeV