Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 41, Problem 4OQ
To determine
Whether the statements are true or false for a photon.
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A quantum particle of mass m is placed in a one-dimensional box of length L. Assume the box is so small that the particle’s motion is relativistic and K = p2/2m is not valid. (a) Derive an expression for the kinetic energy levels of theparticle. (b) Assume the particle is an electron in a box of length L = 1.00 × 10-12 m. Find its lowest possible kinetic energy. (c) By what percent is the nonrelativistic equation in error?
Consider a freely moving quantum particle with mass m and speed u. Its energy is E = K = 1/2mu2. (a) Determine the phase speed of the quantum wave representing the particle and (b) show that it is different from the speed at which the particle transports mass and energy.
(b) An electron confined in a one dimensional box emits a 200 nm photon in a quantum jump from n =
2 to n = 1. What is the length of the box? The mass of an electron is 9.11 x 1031 kg.
(c) A proton confined in a one dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump
from n = 2 to n = 1. What is the length of the box? The mass of a proton is 1.67 x 1027 kg.
Chapter 41 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 41.1 - Prob. 41.1QQCh. 41.2 - Prob. 41.2QQCh. 41.2 - Prob. 41.3QQCh. 41.5 - Prob. 41.4QQCh. 41 - Prob. 1OQCh. 41 - Prob. 2OQCh. 41 - Prob. 3OQCh. 41 - Prob. 4OQCh. 41 - Prob. 5OQCh. 41 - Prob. 6OQ
Ch. 41 - Prob. 7OQCh. 41 - Prob. 8OQCh. 41 - Prob. 9OQCh. 41 - Prob. 10OQCh. 41 - Prob. 1CQCh. 41 - Prob. 2CQCh. 41 - Prob. 3CQCh. 41 - Prob. 4CQCh. 41 - Prob. 5CQCh. 41 - Prob. 6CQCh. 41 - Prob. 7CQCh. 41 - Prob. 8CQCh. 41 - Prob. 1PCh. 41 - Prob. 2PCh. 41 - Prob. 3PCh. 41 - Prob. 4PCh. 41 - Prob. 5PCh. 41 - Prob. 6PCh. 41 - Prob. 7PCh. 41 - Prob. 8PCh. 41 - Prob. 9PCh. 41 - Prob. 10PCh. 41 - Prob. 11PCh. 41 - Prob. 12PCh. 41 - Prob. 13PCh. 41 - Prob. 15PCh. 41 - Prob. 16PCh. 41 - Prob. 17PCh. 41 - Prob. 18PCh. 41 - Prob. 19PCh. 41 - Prob. 20PCh. 41 - Prob. 21PCh. 41 - Prob. 22PCh. 41 - Prob. 23PCh. 41 - Prob. 24PCh. 41 - Prob. 25PCh. 41 - Prob. 26PCh. 41 - Prob. 27PCh. 41 - Prob. 28PCh. 41 - Prob. 29PCh. 41 - Prob. 30PCh. 41 - Prob. 31PCh. 41 - Prob. 32PCh. 41 - Prob. 33PCh. 41 - Prob. 34PCh. 41 - Prob. 36PCh. 41 - Prob. 37PCh. 41 - Prob. 38PCh. 41 - Prob. 39PCh. 41 - Two particles with masses m1 and m2 are joined by...Ch. 41 - Prob. 41PCh. 41 - Prob. 42PCh. 41 - Prob. 43APCh. 41 - Prob. 44APCh. 41 - Prob. 45APCh. 41 - Prob. 46APCh. 41 - Prob. 47APCh. 41 - Prob. 48APCh. 41 - Prob. 49APCh. 41 - Prob. 50APCh. 41 - Prob. 51APCh. 41 - Prob. 52APCh. 41 - Prob. 53APCh. 41 - Prob. 54APCh. 41 - Prob. 56APCh. 41 - Prob. 57APCh. 41 - Prob. 58APCh. 41 - Prob. 59CPCh. 41 - Prob. 60CPCh. 41 - Prob. 61CPCh. 41 - Prob. 62CPCh. 41 - Prob. 63CP
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- For a quantum particle of mass m in the ground state of a square well with length L and infinitely high walls, the uncertainty in position is Δx ≈ L. (a) Use the uncertainty principle to estimate the uncertainty in its momentum.(b) Because the particle stays inside the box, its average momentum must be zero. Its average squared momentum is then ⟨p2⟩ ≈ (Δp)2. Estimate the energy of the particle. (c) State how the result of part (b) compares with the actual ground-state energy.arrow_forward(a) An electron confined in a one-dimensional box is observed, at different times, to have energies of 12 ev, 27 ev, and 48 eV. What is the length of the box? The mass of an electron is 9.11 x 1031 kg. (b) An electron confined in a one dimensional box emits a 200 nm photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of an electron is 9.11 x 1031 kg. (c) A proton confined in a one dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump from n = 2 to n = 1. What is the length of the box? The mass of a proton is 1.67 x 1027 kg.arrow_forwardassume that an electron is moving along the x-axis and that you measure its speed to be 20.5*10^6m/s, which can be known with of precision of 0.50%. what is the minimum uncertainty (as allowed by the uncertainty principle in quantum theory )with which you can simultaneously measure the position of the electron along the x-axis?arrow_forward
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