- #1

uxioq99

- 11

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Misplaced Homework Thread

I have been self-studying the MIT 8.04 Introduction to Quantum Mechanics course. This question is not graded, so I have no reservation asking about it on the internet.

Imagine an electron bound by tritium (Z=1). One of the two neutrons undergoes beta decay and becomes a proton, causing the atom to become helium (Z=2). This process happens so quickly that the wave function of the electron is not changed by the process. If the electron is originally in the ground state of tritium, what is the probability that it will be in the ground state of helium after the decay?

My confusion primarily lies with the concept of an electron being "in" an orbital. Although the admissibility of the solution (i.e., energy conservation) leads to a truncation of the Laguerre polynomials and energy discretization, I thought that orbitals were dictated by their wave functions. Then, because the wave functions admit continuous probability distributions, I would think that belonging to an orbital would be more a spectrum than a dichotomy. On the other hand, I recall diagrams of the Laplacian spherical harmonics and their role in producing the wave functions. If I remember correctly, the fact that they were drawn as two dimensional surfaces was more of an artifact of plotting them cleaning.

Before I attempt to answer the question, I would like to crystallize my understanding of the mathematical description of an electron belonging to an orbital.

Thank you all in advance.

Imagine an electron bound by tritium (Z=1). One of the two neutrons undergoes beta decay and becomes a proton, causing the atom to become helium (Z=2). This process happens so quickly that the wave function of the electron is not changed by the process. If the electron is originally in the ground state of tritium, what is the probability that it will be in the ground state of helium after the decay?

My confusion primarily lies with the concept of an electron being "in" an orbital. Although the admissibility of the solution (i.e., energy conservation) leads to a truncation of the Laguerre polynomials and energy discretization, I thought that orbitals were dictated by their wave functions. Then, because the wave functions admit continuous probability distributions, I would think that belonging to an orbital would be more a spectrum than a dichotomy. On the other hand, I recall diagrams of the Laplacian spherical harmonics and their role in producing the wave functions. If I remember correctly, the fact that they were drawn as two dimensional surfaces was more of an artifact of plotting them cleaning.

Before I attempt to answer the question, I would like to crystallize my understanding of the mathematical description of an electron belonging to an orbital.

Thank you all in advance.