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 46AP
(a)
To determine
De Broglie wavelength of neutron having kinetic energy
(b)
To determine
Check whether the answer of part (a) is comparable with the interatomic spacing of crystal.
(c)
To determine
Check whether the thermal neutrons can exhibit diffraction effects in crystal or not.
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The neutron has a mass of 1.67 ✕ 10-27 kg. Neutrons emitted in nuclear reactions can be slowed down via collisions with matter. They are referred to as thermal neutrons once they come into thermal equilibrium with their surroundings. The average kinetic energy (3kB T/2) of a thermal neutron is approximately 0.04 eV.Calculate the de Broglie wavelength of a neutron with a kinetic energy of 0.0980 eV.
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An alpha particle (m = 6.64 × 10−27 kg) emitted in the radioactive decay of Uranium-238 has an energy of 4.20 MeV. What is its de Broglie wavelength?
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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- Alpha particles of mass m = 6.64 ✕ 10−27 kg and kinetic energy K = 905 keV are projected at a target nucleus. If the alpha particles have a de Broglie wavelength with the same value as the diameter of the target nucleus, determine the radius (in m) of the target nucleus.arrow_forwardThe average energy of a photon in a pulsed laser beam is 2.39 eV, with a minimum uncertainty of 0.0155 eV. Each pulse has an average of 5.00 x 1012 photons. Find (a) the time duration of each pulse, (b) the wavelength of the light, and (c) the energy per pulse in J.arrow_forwardThe existence of the atomic nucleus was discovered in 1911 by Ernest Rutherford, who properly interpreted some experiments in which a beam of alpha particles was scattered from a metal foil of atoms such as gold. (a) If the alpha particles had a kinetic energy of 7.5 MeV, what was their de Broglie wavelength? (b) Explain whether the wave nature of the incident alpha particles should have been taken into account in interpreting these experiments. The mass of an alpha particle is 4.00 u (atomic mass units), and its distance of closest approach to the nuclear center in these experiments was about 30 fm. (The wave nature of matter was not postulated until more than a decade after these crucial experiments were first performed.)arrow_forward
- A photon with wavelength X scatters off an electron at rest, at an angle with the incident direction. The Compton wavelength of the electron Ac = 0.0024 nm. a) For λ = 0.0006 nm and 0 = 53 degrees, find the wavelength X' of the scattered photon in nanometres. b) Obtain a formula for the energy of the electron Ee after collision, in terms of the universal constants h, c and the variables X, X' and Ac. The answer must be expressed in terms of these variables only. (Please enter an algebraic expression using latex format; do not input any numerical values) c) Using the energy conservation condition, find the value of the electron energy Ee after scattering in units of keV. d) Write an algebraic expression for the electron's momentum pe in terms of its energy Ee, its mass me and the speed of light c. e) What is the de Broglie wavelength of the scattered electron ? Express your answer in terms of Ee, me, and X and c. f) Find the value of the de Broglie wavelength of the scattered electron…arrow_forwardT1arrow_forwardA neutron with a potential energy of U = 0 is represented by the wave function y = Ae'(kx – ot) where k = 5.23 × 1010 m-1. (a) What is the momentum (in kg · m/s) of the neutron? kg • m/s (b) What is the kinetic energy (in eV) of the neutron? ev (c) We wish to verify if the given wave function is a solution to Schrödinger's equation. To do this, calculate the following. (Use the following as necessary: k, w, x, t and A. Do not substitute numerical values; use variables only.) dự dx d?w dx2 Substitute the above two results into Schrödinger's equation and solve for the energy of the particle. (Use the following as necessary: h, k, m, w, x, t and A. Do not substitute numerical values; use variables only.) E = Calculate the energy (in eV) of the neutron. evarrow_forward
- What is the kinetic energy of each electron in a beam of electrons if the beam produces a diffraction pattern of a crystal which is similar to that of a beam of 1.00 eV neutrons? (knowing that electron mass is 9.11*10^-31 kg and neutron mass is 1.67*10^-26 kg). What are the specific equations that are being used in this problem?arrow_forwardThe de Broglie wavelength of an electron has to do with spatial resolution of an electron microscope, which is often expressed in the unit of length Å (Angstrom). The 1 V potential difference causes an electron to gain kinetic energy EK of 1 electron Volt (eV). In the SI units, kinetic energy in eV must be converted to Joules. The conversion factor is 1 eV = 1.6 x 10-19 Joule. And, the formula for the wavelength is: λ = h / p = h / √(2 m EK) where m is electron mass. Calculate the de Broglie wavelength of an electron (in Å) when the electron is accelerated from rest through a potential difference of: a) 1 kV = 1,000 V (a low resolution setting of microscope), b) 10 kV = 10,000 V (intermediate resolution). c) 100 kV = 100,000 V (high resolution),arrow_forwardSuppose a star with radius 8.51 108 m has a peak wavelength of 689 nm in the spectrum of its emitted radiation. (a) Find the energy of a photon with this wavelength. J/photon(b) What is the surface temperature of the star? K(c) At what rate is energy emitted from the star in the form of radiation? Assume the star is a blackbody (e = 1). W(d) Using the answer to part (a), estimate the rate at which photons leave the surface of the star. photons/sarrow_forward
- A thermal neutron with mass of 1.67 x 10^-27 kg travels at a speed of 2200 m/s. Calculate the de Broglie wavelength.arrow_forwardWhat are the (a) energy, (b) magnitude of the momentum, and (c) wavelength of the photon emitted when a hydrogen atom undergoes a transition from a state with n = 4 to a state with n = 2? (a) Number 2.55 Units eV (b) Number 1.3617 Units kg-m/s or N-s (c) Number 4.865976353 Units This answer has no unitsarrow_forwardThe electron beam in a scanning electron microscope (SEM) can have an energy ranging from 0.2 keV to 40 keV. (Note: an eV is an electronvolt, the measure of an amount of kinetic energy for a single electron. 1 eV = 1.60218×10−19 J and 1 J = 1 kg m2 s−2). What is the de Broglie wavelength of the electron beam in the SEM when the electrons are accelerated to kinetic energy of 6.6 keV?arrow_forward
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