Orbital Quantum Numbers And Total Electron Energy

Hello 🙂

1. The problem statement, all variables and given/known data

The orbital quantum number for the electron in the hydrogen atom is l = 4. What
is the smallest possible value (in eV) for the total energy of this electron? (Use the
quantum mechanical model of the hydrogen atom.)

2. Relevant equations

3. The attempt at a solution

I know that the angular momentum of the electron is given by;

[itex]L = \sqrt{l(l + 1)}\frac{h}{2 \pi}[/itex]

[itex]L = \sqrt{20} \frac{h}{2 \pi}[/itex]

L = 4.64×10-33 Kgm2s-1

My text book doesn’t really discuss the QM picture of the atom, so I don’t know how to relate this to the energy of the electron.

I know how to do it for the Bohr model, but clearly that’s no good.

I appreciate any help you can give,



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