PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
6th Edition
ISBN: 9781429206099
Author: Tipler
Publisher: MAC HIGHER
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Chapter 35, Problem 23P
To determine
The ground state energy of ten non interacting bosons in one dimensional box.
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Most of the particles known to physicists are unstable. For example, the lifetime of the neutral pion,π0, is about 8.4x10-17 s. Its mass is 135.0 MeV/c2. a) What is the energy width of the π0 in its ground state? b) What is the relative uncertainty ∆m/m of the pion’s mass?
Chapter 35 Solutions
PHYSICS F/SCI.+ENGRS.,STAND.-W/ACCESS
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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- The neutral pion nº is an unstable subatomic particle with a mass of 135.0 MeV/c² and a lifetime of about 8.4 x 10-17 s. What is the uncertainty of the energy of the nº in its ground state? What is the relative uncertainty Am/m of its mass?arrow_forwardThe range of the nuclear strong force is believed to be about 1.2 x 10-15 m. An early theory of nuclear physics proposed that the particle that “mediates” the strong force (similar to the photon mediating the electromagnetic force) is the pion. Assume that the pion moves at the speed of light in the nucleus, and calculate the time ∆t it takes to travel between nucleons. Assume that the distance between nucleons is also about 1.2 x 10-15 m. Use this time ∆t to calculate the energy ∆E for which energy conservation is violated during the time ∆t. This ∆E has been used to estimate the mass of the pion. What value do you determine for the mass? Compare this value with the measured value of 135 MeV/c2 for the neutral pion.arrow_forwardUnder the right circumstances, a photon of high enough energy can give rise to an electron-positron pair. What minimum energy photon is required?arrow_forward
- A particle in a one-dimensional box of length L has a kinetic energy much greater than its rest energy. What is the ratio of the following energy levels En: E2/E1, E3/ E1, E4/E1? How do your answers compare with the nonrelativistic case?arrow_forwardHow does the relativistic landau energy spectrum for a particle in a magnetic field simplify down in the non-relativistic limit?arrow_forwardProvide the answers in 90 minutes, and count as 2 questions if needed.arrow_forward
- A photon beam (2λ = 1.00 pm) is incident on a sphere with radius 1.00 mm. It has energy 100 MeV. a. Assuming that within the sphere there are 1000 type A-interactions, what is the cross section of this type-A interaction? b. Assuming that within the sphere there are 2000 type B-interactions, what is the cross section of this type-B interaction?arrow_forwardThe Z0 boson, discovered in 1985, is the mediator ofthe weak nuclear force, and it typically decays very quickly.Its average rest energy is 91.19 GeV, but its short lifetimeshows up as an intrinsic width of 2.5 GeV. What is the lifetime of this particle?arrow_forwardIf pair production of muon-antimuon pair can occur for photons of wavelength = 5.85 x 10-15m or less, what is the mass of a muon?arrow_forward
- The energy of the four non-interacting identical fermions and bosons in one dimensiona! box of size a is, 5h? 4h? (a) ma² ' 2ma? 5h? 2h? (b) ma ' ma 10h? 3h? (c) 2ma' 2ma? 2h? 4h? (d) ma² ' 2ma?arrow_forwardThe average lifetime of a tau is about 2.9 ✕ 10−13 s. Estimate the minimum uncertainty in the energy of a tau. Jarrow_forwardA π0 meson is an unstable particle produced in high-energy particle collisions. Its rest energy is approximately 135 MeV, and it exists for a lifetime of only 8.70 × 10-17 s before decaying into two gamma rays. Using the uncertainty principle, estimate the fractional uncertainty Δm/m in its mass determination.arrow_forward
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