Ist-order binomial approximation: (1+x)"≈1+nx. The second-order approximation keeps the second-order term, 2nd-order binomial approximation: (1+x)" ≈ 1+nx+ n(n − 1) x², - 2!
Q: Two π+ mesons are created. One is created at rest in the laboratory, and one moving at v = (4/5)c. c…
A: Given : Let us say that π1 is created at rest in the laboratory frame and π2 is the one which is…
Q: The K+ meson, a subatomic particle, has an average rest lifetime of 1.0 x 10-8 s. If the particle…
A: The time interval for an event measured in a moving inertial frame is related to the time interval…
Q: Find the proper lifetime of that particle: to= .000000000381 X s.
A:
Q: The average lifetime of mu-meson is 2.19698-106 s. These subatomic particles are produced high in…
A:
Q: A K⁻ meson has a rest lifetime of 1.24 x 10⁻⁸ s. If one of these particles is created in a particle…
A: Formula of time dilation is as follows: ∆t'=∆t1-v2c2…
Q: A particle has a proper lifetime of 2.5 × 10^−6s. How fast/gamma must it be going to arrive on the…
A: To calculate the speed and gamma factor of the particle, we need to use the formula: γ = 1/√(1 -…
Q: When a star erupts in a supernova explosion, huge numbers of electron neutrinos are formed in…
A:
Q: In the first upgrade of the Large Hadron Collider, each of the colliding proton beams was designed…
A: When an object is moving with a velocity comparable to that of light relativistic effects should be…
Q: What is the rest energy of a positive kaon, given its mass is 8.80 ✕ 10−28 kg? Give your answer in…
A:
Q: A new particle, the joelon, has just been discovered! Careful measurements show that the joelon has…
A:
Q: A supernova explosion of a 1.25 × 1031 kg star produces 1.9 × 1044 J of energy. Randomized…
A:
Q: Provide the answers in 2 hours, and count as 2 questions if necessary.
A: Step 1: a) The mechanism responsible for the energy loss in this electron-positron collider is…
Q: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…
A: Given Data: Average life time of pi meson (∆t) = 2.6×10-8 s.Speed of the pi meson (v) = 0.93c. To…
Q: Say that the mean lifetime of a π+ meson in its own rest frame is τ = 2.6 x 10-8 s. A pion of this…
A:
Q: (a) What is the effective accelerating potential for electrons at the Stanford Linear Accelerator,…
A:
Q: The neutron has a mass of 1.67 ✕ 10−27 kg. Consider a neutron moving with a speed of 0.910c. (Enter…
A: Given:- The proton has a mass m = 1.67 ✕ 10−27 kg a proton moving with a speed of 0.910c
Q: High-energy particles are observed in laboratories by photographing the tracks they leave in certain…
A:
Q: A neutral -meson is a particle that can be created by accelerator beams. If one such particle lives…
A:
Q: The lifetime of a muon is 2.20 ?s. If you measured its mass to be 105.7 MeV/c2, what would be the…
A: According to Heisenberg's uncertainty principle, the product of uncertainties of a canonical pair of…
Q: Consider that a particle of mass m decays into two particles of mass m1 and m2, and the first…
A: π+ → µ+ + νµMπ+=0.1396 GeV, m µ=0.1057 GeV and mv =0We need to find out: The Energy and Momentum of…
Q: What is the rest energy (in joules) of a subatomic particle whose (rest) mass is 6.7×10−31 kg? How…
A: Rest mass m0=6.7×10^-31 kg Rest mass energy E=m0C2 C=3×10^8 m/s
Q: A particle is propagating at relativistic speed. It is observed to have an energy of 3.1 GeV and a…
A: Given, The energy of the particle, E=3.1 GeV=3.1×109×1.6×10-19=4.96×10-10 J The momentum of the…
Q: Two distant galaxies are observed to have redshifts z₁ = 0.05 and 22 = 0.15, and distances d₁ =…
A: Red sifts for two distant galaxies: z1=0.05z2=0.15 The distances are: d1=220.60 Mpcd2=661.75 Mpc
Q: While in flight, an unstable particle decays into three pions (rest mass 140 MeV/c²) according to…
A:
Q: (ii) An electron e- having kinetic energy 1.0 MeV has a head-on collision with a positron e* at…
A: 5. (ii) The energy momentum relation is given as, E2=p2c2+mc22 where Eis the total energy of the…
Q: The center of our Milky Way galaxy is about 23000 ly away. (a) To eight significant figures, at what…
A:
Q: A particle is propagating at relativistic speed. It is observed to have an energy of 3.1 GeV and a…
A: Given data: Energy E = 3.1 GeV Momentum p=7.34×10-19 kg.m/s
Q: lve the following problem using Lorentz transformations: Two jets of material are ejected in…
A: Given:- Two jets of material are ejected in opposite directions from the center of a radio galaxy.…
Q: A beam of π+meson (pions) at Fermilab are traveling at a speed of 0.92cwithrespect to the…
A:
Q: leave Earth, the Trappist-1 system might make a good destination – the star there has seven…
A:
Q: The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6…
A: Meson Particles Meson Particles are the hadronic subatomic particles that have an equal number of…
Say that the mean lifetime of a π+ meson in its own rest frame is τ = 2.6 x 10-8 s. A pion of this lifetime is created at an altitude 100 km in the atmosphere by the collision of an incoming cosmic·ray proton with an atmospheric nucleus, and it has lifetime τ.
Use the binomial approximation (see attached image) to determine how fast would this π+ meson need to move in order to reach the ground before decaying. Express the velocity in the form v/c = 1 - ϵ, where ϵ << 1.
Step by step
Solved in 2 steps with 2 images
- Two distant galaxies are observed to have redshifts z1 = 0.05 and z2 = 0.15, and distances d1 = 220.60 Mpc and d2 = 661.75 Mpc, respectively. Assuming the motion of the galaxies is due to the Hubble flow, determine the value of the Hubble constant, H0. Show how the value of H0 can be used to estimate the age of the Universe, describing any assumptions that you make. Use the value of H0 you have obtained to estimate the age of the Universe, expressing your answer in Gyr.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.
- A new theory predicts that a chargino x¯ of mass m(x¯¯) = 620 GeV decays into a neutralino x with a mass of m(x) = 171 GeV and a W boson with a mass of m(W) 80.4 GeV. a) Calculate the energy of the neutralino in the rest frame of the chargino.Calculate the lifetime in s of an exotic particle with a rest energy of 83.67 ± 1.93 GeV.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.
- What is the kinetic energy in MeV of a π -meson that lives 1.40×10−16 s as measured in the laboratory, and 0.840×10−16 s when at rest relative to an observer, given that its rest energy is 135 MeV?Consider a cosmic ray colliding with a nucleus in the Earth's upper atmosphere that produces a muon which has a velocity v = 0.916c. The muon then travels at constant velocity and lives 1.52 µs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.) (a) How far (in km) does the muon in travel according to an Earth-bound observer? (b) How far (in km) does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to the Earth and the time it lives (proper time).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