Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 39, Problem 30P
(a)
To determine
Show that
(b)
To determine
Whether it is possible for a particle of nonzero mass to have equal wavelength and frequency like 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?
(a) Show that the frequency f and wavelength λ of a freely moving quantum particle with mass are related by the expression (F/c)2 = 1/λ2 + 1/λC2where λC = h/mc is the Compton wavelength of the particle. (b) Is it ever possible for a particle having nonzero mass to have the same wavelength and frequency as a photon? Explain.
(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 39 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 39.1 - Prob. 39.1QQCh. 39.2 - Prob. 39.2QQCh. 39.2 - Prob. 39.3QQCh. 39.2 - Prob. 39.4QQCh. 39.3 - Prob. 39.5QQCh. 39.5 - Prob. 39.6QQCh. 39.6 - Prob. 39.7QQCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3P
Ch. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 35PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40APCh. 39 - Prob. 41APCh. 39 - Prob. 43APCh. 39 - Prob. 44APCh. 39 - Prob. 45APCh. 39 - Prob. 46APCh. 39 - Prob. 47CPCh. 39 - Prob. 48CPCh. 39 - Prob. 49CPCh. 39 - Prob. 50CP
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- A quantum mechanical oscillator vibrates at a frequency of 250.0 THz. What is the minimum energy of radiation it can emit?arrow_forward(a) Calculate the wavelength (in m) of a photon that has the same momentum as a proton moving at 1.21% of the speed of light. m (b) What is the energy of the photon in MeV? MeV (c) What is the kinetic energy of the proton in MeV? MeVarrow_forward(a) If the wavelength of an electron is 5.33 x 10-7 m, how fast is it moving? 0.58 X Your response differs from the correct answer by more than 10%. Double check your calculations. km/s (b) If the electron has a speed equal to 5.00 x 106 m/s, what is its wavelength? marrow_forward
- What velocity must an electron travel with for its momentum to equal that of a photon with a wavelength of λ = 520 nm?arrow_forwardAn atom in an excited state of 4.7 eV emits a photon and ends up in the ground state. The lifetime of the excited state is 1.0 x 10-13 s. (a) What is the energy uncertainty of the emitted photon? (b) What is the spectral line width (in wavelength) of the photon?arrow_forwardWhat speed must an electron have if its momentum is to be the same as that of an X-ray photon with a wavelength of 0.35 nm?arrow_forward
- An electron is accelerated from rest through a potential difference of 3.19 x 102 V. Determine the following for the electron. (a) speed (ignore relativistic effects) m/s (b) de Broglie wavelength marrow_forwardThe minimum uncertainty Ay in the position y of a particle is equal to its de Broglie wavelength. Determine the minimum uncertainty in the speed of the particle, where this minimum uncertainty Avy is expressed as a percentage of the particle's speed vy Avv Percentage = 6)... . Assume that relativistic effects can be ignored. Uy Number i x 100 % Unitsarrow_forwardA 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?arrow_forward
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