Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Chapter 39, Problem 72GP
To determine
The comparison between the
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Two electrons in the same atom have n = 3 and ℓ = 1. (a) List the quantum numbers for the possible states of the atom. (b) How many states would be possible if the exclusion principle did not apply to the atom?
Show that the wave function ψ100 of the hydrogen atom provides the Schrödinger equation.
What are the most significant differences between the Bohr model of the hydrogen atom and the Schrödinger analysis? What are the similarities?
Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 39.2 - Prob. 1AECh. 39.2 - Prob. 1BECh. 39.3 - Prob. 1CECh. 39.4 - Prob. 1DECh. 39.4 - Prob. 1EECh. 39.5 - Prob. 1FECh. 39.7 - Prob. 1GECh. 39 - Prob. 1QCh. 39 - Prob. 2QCh. 39 - Prob. 3Q
Ch. 39 - Prob. 4QCh. 39 - Prob. 5QCh. 39 - Prob. 6QCh. 39 - Prob. 7QCh. 39 - Prob. 8QCh. 39 - Prob. 9QCh. 39 - Prob. 10QCh. 39 - Prob. 11QCh. 39 - On what factors does the periodicity of the...Ch. 39 - Prob. 13QCh. 39 - Prob. 14QCh. 39 - Prob. 15QCh. 39 - Prob. 16QCh. 39 - Prob. 17QCh. 39 - Prob. 18QCh. 39 - Prob. 19QCh. 39 - Prob. 20QCh. 39 - Prob. 21QCh. 39 - Prob. 22QCh. 39 - Prob. 23QCh. 39 - Prob. 24QCh. 39 - Prob. 25QCh. 39 - Prob. 26QCh. 39 - Prob. 27QCh. 39 - Prob. 28QCh. 39 - Prob. 29QCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3PCh. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 7PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 14PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 21PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 28PCh. 39 - Prob. 29PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 34PCh. 39 - Prob. 35PCh. 39 - Prob. 36PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40PCh. 39 - Prob. 41PCh. 39 - Prob. 42PCh. 39 - Prob. 43PCh. 39 - Prob. 44PCh. 39 - Prob. 45PCh. 39 - Prob. 46PCh. 39 - Prob. 47PCh. 39 - Prob. 48PCh. 39 - Prob. 49PCh. 39 - Prob. 50PCh. 39 - Prob. 51PCh. 39 - Prob. 52PCh. 39 - Prob. 53PCh. 39 - Prob. 54PCh. 39 - Prob. 55PCh. 39 - Prob. 56PCh. 39 - Prob. 57PCh. 39 - Prob. 58PCh. 39 - Prob. 59PCh. 39 - Prob. 60PCh. 39 - Prob. 61GPCh. 39 - Prob. 62GPCh. 39 - Prob. 63GPCh. 39 - Prob. 64GPCh. 39 - Prob. 65GPCh. 39 - Prob. 66GPCh. 39 - Prob. 67GPCh. 39 - Prob. 68GPCh. 39 - Prob. 69GPCh. 39 - Prob. 70GPCh. 39 - Prob. 71GPCh. 39 - Prob. 72GPCh. 39 - Prob. 73GPCh. 39 - Prob. 74GPCh. 39 - Prob. 75GPCh. 39 - Prob. 76GPCh. 39 - Prob. 77GP
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- Two electrons in the same atom have n = 3 and l = 1. (a) List the quantum numbers for the possible states of the atom. (b) How many states would be possible if the exclusion prin- ciple did not apply to the atom?arrow_forwardWhat is the value N so that ψ(x) = N/(a2 + x2) can give rise to a valid probability density?arrow_forwardWhat is the maximum photon wavelength that would free an electron in a hydrogen atom when it is in the n = 8 excited state? (Give the answer in meters.)arrow_forward
- In the Bohr model, what is the principal quantum number n at which the excited electron is at a radius of 1 mm?arrow_forwardShow that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum number of the atom.arrow_forwardDetermine whether Ψ(x, t) = A sin(kx - ωt) is an acceptable solution to the time-dependent Schrödinger wave equation.arrow_forward
- 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_forwardEstimate the size of the Bohr atom by using uncertainty arguments and minimizing the energy.arrow_forwardCalculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 x 108 m as the average Earth–Moon distance and 2.36 x 106 s as the period of the Moon in its orbit. (b) If the angular momentum of the Moon obeys Bohr’s quantization rule (L = n h), determine the value of the quantum number n. (c) By what fraction would the Earth–Moon radius have to be increased to increase the quantum number by 1?arrow_forward
- When an electron in hydrogen atom jumps from the third excited state to the ground state, how would the de Broglie wavelength associated with the electron change? Justify your answer.arrow_forwardA negatively charged muon (µ¯) has the same charge as as electron, but it is heavier. Imagine a hydrogen-like atom in which the electron is replaced by a muon. Such atoms are called muonic atoms, and they can be produced in the laboratory. Assume that such an atom can be described in the same way as the normal Bohr atom. (a) What is the ground state energy of a muonic hydrogen atom? (b) What is the radius of the muon's orbit in the ground state of a muonic hydrogen atom? (c) What is the radius of the muon's orbit in the ground state of a muonic lead atom (Z = 82), i.e., a lead nucleus with one muon (and no electrons) orbiting it? Compare this with the radius of the lead nucleus (about 7 fm). What does this tell you about the muon's "orbital path?"arrow_forwardUse the Bohr theory to estimate the wavelength for an n = 3 to n = 1 transition in molybdenum. The measured value is 0.063 nm. Why do we not expect perfect agreement?arrow_forward
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