Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 3, Problem 40P
(a)
To determine
The proof for the given relation.
(b)
To determine
Prove the relation for
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(a) Calculate the speed of an electron that is in the n = 1 orbit of a hydrogen atom, and give your answerv as a fraction of the speed of light in empty space c, for example, v = 0.5 if the answer werev = c/2 = 1.50 × 108 m/s. (It isn’t.)(b) How many nanometers would be the wavelength of the photon emitted when the electron in a hydrogenatom jumps from the n = 3 orbit to the n = 2 orbit? This is the Hα line, and its light is scarlet, the color offresh human blood.(c) How many nanometers would be the wavelength of the photon emitted when the electron in a hydrogenatom jumps from the n = 2 orbit to the n = 1 orbit?(d) How many nanometers would be the wavelength of a photon that would have the minimum amount ofenergy needed to ionize any hydrogen atom? (Hint: Electromagnetic radiation with this wavelength or shorteris called extreme ultraviolet radiation.(e) How many electron-volts (eV) would the electron in part (7)(d) need to have?
(a) Use the appropriate Uncertainty Principle to calculate the linewidth uncertainty in units of Hz, for an optical emission transition that has a lifetime of τ = 10−9 s.
(b) Use calculus to show that an emission transition that has a linewidth of ∆f in frequency, has a linewidth in wavelength given by ∆λ = −(λ^2)/c * ∆f
(c) What would be the linewidth in nm, of a transition at 600 nm if it had the lifetime given in part (a)?
When an atom emits a photon in a transition from a state of energy E1 to a state of energy E2, the photon energy is not precisely equal to E1-E2. Conservation of momentum requires that the atom must recoil, and so some energy must go into recoil kinetic energy KR. Show that KR is roughly equal to (E1-E2)2/2Mc2, where M is the mass of the atom. Evaluate this recoil energy for the n=2 to n=1 transition of hydrogen.
Chapter 3 Solutions
Modern Physics
Ch. 3.2 - Calculate the quantum number, n, for this pendulum...Ch. 3.2 - An object of mass m on a spring of stiffness k...Ch. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8Q
Ch. 3 - Prob. 9QCh. 3 - Prob. 10QCh. 3 - Prob. 11QCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - As a single crystal is rotated in an x-ray...Ch. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48P
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