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 40.2, Problem 40.2QQ
(i)
To determine
The particle having highest energy in ground state.
(ii)
To determine
The particle having longest wavelength in ground state.
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Consider an electron, a proton, and an alpha particle (a helium nucleus), each trapped separately in identical boxes.
(i) Which particle corresponds to the highest ground-state energy?
(ii) which particle have longest wavelength when system is in ground state.
In an electron microscope, the nonrelativistic electron beam is formed by a setup similar to the electron gun used in the Davisson– Germer experiment. The electrons have negligible kinetic energy before they are accelerated. What accelerating voltage is needed to produce electrons with wavelength 10 pm = 0.010 nm (roughly 50,000 times smaller than typical visible-light wavelengths)?
A scientist wants to use an electron microscope to observe details on the order of 0.25 nm.
Through what potential difference must the electrons be accelerated from rest so that they have a de Broglie wavelength of this magnitude?
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
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- (a) In an electron microscope, what accelerating voltage is needed to produce electrons with wavelength 0.0600 nm? (b) If protons are used instead of electrons, what accelerating voltage is needed to produce protons with wavelength 0.0600 nm?arrow_forwardThe nucleus of a typical atom is 5.0 fm (1 fm = 10-15 m) in diameter. A very simple model of the nucleus is a onedimensional box in which protons are confined. Estimate the energy of a proton in the nucleus by finding the first three allowed energies of a proton in a 5.0-fm-long box.arrow_forward(a) If a photon and an electron each have the same energy of 20.0 eV, find the wavelength of each. (b) If a photon and an electron each have the same wavelength of 250 nm, find the energy of each. (c) You want to study an organic molecule that is about 250 nm long using either a photon or an electron microscope. Approximately what wavelength should you use and which probe, the electron or the photon, is likely to damage the molecule the least?arrow_forward
- An 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_forwardAn electron confined to a box absorbs a photon with wavelength λ. As a result, the electron makes a transition from the n = 1 state to the n = 3 state. (a) Find the length of the box. (b) What is the wavelength λ' of the photon emitted when the electron makes a transition from the n = 3 state to the n = 2 state?arrow_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
- Consider an electron, a proton, and an alpha particle (a helium nucleus), each trapped separately in identical boxes. (i) Which particle corresponds to the highest ground-state energy? Also which particle have longest wavelength when system is in ground statearrow_forwardThrough what minimum potential difference must an electron in an x-ray tube be accelerated so that it can produce x rays with a wavelength of 0.100 nm?arrow_forwardA general expression for the energy levels of oneelectron atoms and ions is Here µ is the reduced mass of the atom, given by µ = m1m2/(m1 +m2m2), where m1 is the mass of the electron and m2 is the mass of the nucleus; ke is the Coulomb constant; and q1 and q2 are the charges of the electron and the nucleus, respectively. The wavelength for the n = 3 to n = 2 transition of the hydrogen atom is 656.3 nm (visible red light). What are the wavelengths for this same transition in (a) positronium, which consists of an electron and a positron, and (b) singly ionized helium? Note: A positron is a positively charged electron.arrow_forward
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