When calculating the orbital energy of an electron in a hydrogen-like atom, the orbital velocity is required. However, to derive this value, the equation given is: Z K_e (e^2)/(r^2) and K_e is the atomic number.

Brylee Shepard

Brylee Shepard

Answered question

2022-08-14

When calculating the orbital energy of an electron in a hydrogen-like atom, the orbital velocity is required. However, to derive this value, the equation given is:
Z K e e 2 / r 2 and K e
is the atomic number. However, there are plenty of systems that behave with an electron orbital which are non-atomic, like those have an quantum potential well. In these cases, there is no single defined atomic number, so how would one go off calculating this?

Answer & Explanation

Jazmyn Bean

Jazmyn Bean

Beginner2022-08-15Added 18 answers

If you have a quantum system, you use the mechanism of quantum mechanics. You solve the Schrodinger equatons with the specific potential. For hydrogen atom you use the Coulomb potential, for a potential well you use whatever function describes your potential well. No orbital velocity is required in either case. The solutions of the Schrodinger equation are the wave functions for all possible states. With the wave functions you can calcuate the energies for any specific state, if this is what you want. If you mean to use the calssical approach used in the Bohr model of the atom, this is not valid for a quantum system. The main reason the QM was developed.

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