Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 35, Problem 7FTD
To determine
Whether any of the energy levels are degenerate for a particle confined in two-dimensional box with sides are in the ratio
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Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 250C.a) Use the model of a particle in a box and assume the particle is at the state: n = nx = ny = nz, calculate n of the above system. b) What is the energy separation between the states (n, n, n) and (n + 1, n, n).
For a moment, assume that there are electrons in the nucleus. The radius of the
nucleus is of the order of 1 fm. What would be the minimum momentum of these
electrons? What would be the minimum kinetic energy of these electrons?
An alpha particle of mass 3727.4 x 106 eV/c² is trapped in a box of size L = 0.000001 nm = 106 nm (the size of a nucleus). Treat this as a 1D infinite square well. Find:
(a) The n = 5 wavefunction and probability density. Draw a graph.
(b) The ground state energy and first excited state.
(c) The wavelength of a photon emitted when the alpha particle transitions from the first excited state to the ground state. [Note that wavelengths between 0.001 nm to 10 nm are x rays and less than 0.001 nm are gamma rays.]
(d) The probability that the alpha particle is in the range x = 0 to x = 2/5L for the n= 5 state.
(e) The expectation value of the position of the alpha particle for then=5 state. If by inspection, explain.
Chapter 35 Solutions
Essential University Physics (3rd Edition)
Ch. 35.1 - Prob. 35.1GICh. 35.2 - Prob. 35.2GICh. 35.3 - Prob. 35.3GICh. 35.3 - Prob. 35.4GICh. 35.3 - Prob. 35.5GICh. 35.4 - Prob. 35.6GICh. 35 - Prob. 1FTDCh. 35 - Prob. 2FTDCh. 35 - Prob. 3FTDCh. 35 - Prob. 4FTD
Ch. 35 - Prob. 5FTDCh. 35 - Prob. 6FTDCh. 35 - Prob. 7FTDCh. 35 - What did Einstein mean by his re maxi, loosely...Ch. 35 - Prob. 9FTDCh. 35 - Prob. 10FTDCh. 35 - Prob. 12ECh. 35 - Prob. 13ECh. 35 - Prob. 14ECh. 35 - Prob. 15ECh. 35 - Prob. 16ECh. 35 - Prob. 17ECh. 35 - Prob. 18ECh. 35 - Prob. 19ECh. 35 - Prob. 20ECh. 35 - Prob. 21ECh. 35 - Prob. 22ECh. 35 - Prob. 23ECh. 35 - Prob. 24ECh. 35 - Prob. 25ECh. 35 - Prob. 26ECh. 35 - Prob. 27ECh. 35 - Prob. 28ECh. 35 - Prob. 29ECh. 35 - Prob. 30ECh. 35 - Prob. 31ECh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38PCh. 35 - Prob. 39PCh. 35 - Prob. 40PCh. 35 - Prob. 41PCh. 35 - Prob. 42PCh. 35 - Prob. 43PCh. 35 - Prob. 44PCh. 35 - Prob. 45PCh. 35 - Prob. 46PCh. 35 - Prob. 47PCh. 35 - Prob. 48PCh. 35 - Prob. 49PCh. 35 - Prob. 50PCh. 35 - Prob. 51PCh. 35 - Prob. 52PCh. 35 - Prob. 53PCh. 35 - Prob. 54PCh. 35 - Prob. 55PCh. 35 - Prob. 56PCh. 35 - Prob. 57PCh. 35 - Prob. 58PCh. 35 - Prob. 59PCh. 35 - Prob. 60PCh. 35 - Prob. 61PPCh. 35 - Prob. 62PPCh. 35 - Prob. 63PPCh. 35 - Prob. 64PP
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- Consider an Ar atom trapped in a square box with a length of 1 m. Assume that the energy of the Ar atom is equal to thermal energy: 3kBT/2 at 25 C. Use the model of a particle in a box and assume the particle is at the state: n = nx= ny= nz, calculate n of the above system.arrow_forwardComparisons of the energy differences between two states with that predicted by theory can test the theoretical model. For the case of the muon g-value, there's a small discrepancy between it and the Standard Model of particle physics. We can see atomic transitions in cesium in atomic clocks. We can measure the frequency by applying pulses at frequencies to observe the resonance (see the provided equation, Rabi's formula). Consider a spin-1/2 particle that precesses in a magnetic field in the z direction. The probability of the particle being spin up or spin down along z doesn’t vary with time. The states |+z> and |—z> are stationary states of the Hamiltonian H-hat = ω0 S-hatz. If we alter the Hamiltonian by applying in addition an oscillating magnetic field transverse to the z axis, we can induce transitions between these two states by properly adjusting the frequency of this transverse field. The energy difference E+—E_ = h-bar ω0 can then be measured with high accuracy. This…arrow_forwarda. For the allowed energies of a particle in a box to be large, should the box be very big or very small? Explain.b. Which is likely to have larger values for the allowed energies: an atom in a molecule, an electron in an atom, or a proton in a nucleus? Explain.arrow_forward
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