University12 min

The quantum atom: wavefunction, quantum numbers, energy

The de Broglie relation, the meaning of |ψ|², the bounds of the four quantum numbers and hydrogen-like energies: the base of every atomic-structure problem.

The essentials

1

The de Broglie relation

λ=hp=hmv\lambda = \dfrac{h}{p} = \dfrac{h}{mv} with h=6.626×10−34 J⋅sh = 6.626 \times 10^{-34}\ \text{J·s}, mm in kg, vv in m/s, λ\lambda in m. For an electron bound in an atom, λ\lambda is of the order of 10−10 m10^{-10}\ \text{m}, the size of the atom: speaking of a trajectory no longer makes sense.
2

The Schrödinger equation and the meaning of ψ

Members only

3

The three quantum numbers of an orbital

Members only

4

Spin and the Pauli principle

Members only

5

Energy: hydrogen-like versus many-electron

Members only

ƒWrite my own sheetOr start from a blank page: rewriting a concept in your own words is how it sticks.