Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
Chapter 8, Problem 12P
(a)
To determine
Sketch the graph for wave function versus radial coordinate of the electron.
(b)
To determine
To show that the probability of finding the electron between
(c)
To determine
Sketch the probability versus radial coordinate and calculate the radius at which the electron is most likely to be found.
(d)
To determine
Show that the given wave function is normalised.
(e)
To determine
The probability of locating the electron between
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What features of the Bohr model of hydrogen are consistent with the later, full quantum mechanical analysis?
1. When the atom drops from a higher energy state to a lower energy state, a photon is emitted with the energy corresponding to the difference in energy levels.
2. K+U is (-13.6/N2) eV.
3. The energy is quantized.
4.The electron moves in distinct circular orbits.
5. The angular momentum in the ground state is h/2.
6. The angular momentum is quantized.
7. Higher energy states correspond to a larger size of the atom.
8. A photon can be absorbed by the atom if the photon's energy corresponds to the energy necessary to jump to a higher energy level.
The longest wavelength line of the Balmer Series for hydrogen occurs at 656.3 nm corresponding to the transition from n2 = 3 to n1 = 2. Determine the value for the Rydberg constant for hydrogen using these values.
The wavefunction for an electron in the Hydrogen atom is provided in figure 1, where B is a constant, and a0 is the Bohr radius.
By inspection and using the radial part of the wavefunction, identify the value of the quantum number then, calculate the energy level of this electron (answer in eV).
Chapter 8 Solutions
Modern Physics
Ch. 8.1 - Prob. 1ECh. 8.1 - Prob. 2ECh. 8.3 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8 - Prob. 1QCh. 8 - Prob. 2QCh. 8 - Prob. 3QCh. 8 - Prob. 4QCh. 8 - Prob. 5QCh. 8 - Prob. 6Q
Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 34P
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- For an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the kinetic energy; (c) the potential energy; and (d) the total energy.arrow_forwardFor a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .arrow_forward
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