Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 11.3, Problem 11.16P

(a)

To determine

The decay routes that are open to the hydrogen decays by a sequence of transitions to the ground state.

(b)

To determine

The fraction of a bottle full of atoms in the state |300 that would decay via each route.

(c)

To determine

The lifetime of the states.

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The "Triple-Alpha Process" is a nuclear fusion process that fuses three "He into one 12C, 3 4He → 12C+ energy. (The 4He nucleus is called an "alpha particle," which is related to alpha radiation.) If the nuclei are all in their ground states, and have negligible kinetic energy, how much energy is released in this reaction? Of course, this is not how quantum mechanics works. It's much more likely for this process to occur if the total energy of three "He particles is equal to one of the allowed energy states of 12C. It turns out that there is an excited state of the 12C nucleus, call it 12C*, that is 7.656 MeV above the ground state nucleus. Calculate the mass of 12C* and its binding energy.
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In a scattering experiment, an alpha particle A is projected with the velocity up = -(600 m/s)i + (750 m/s)j - (800 m/s)k into a stream of oxygen nuclei moving with a common velocity vo = (630 m/s)j. After colliding successively with nuclei B and C, particle A is observed to move along the path defined by the Points A₁(280, 240, 120) and A2(360, 320, 160), while nuclei B and Care observed to move along paths defined, respectively, by B₁(147, 220, 130), B2(114, 290, 120), and by C₁(240, 232, 90) and C₂(240, 280, 75). All paths are along straight lines and all coordinates are expressed in millimeters. Knowing that the mass of an oxygen nucleus is four times that of an alpha particle, determine the speed of each of the three particles after the collisions. The speed of particle A is The speed of particle B is The speed of particle Cis m/s. m/s. m/s.
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