Quantum Mechanics 1: Hydrogen Atom and Atomic Structure

What are the four quantum numbers that correspond to the 3d8 electron?

When $n = 3$ and $L = 0$, calculate the total number of orbitals for the subshells $n = 3, L = 0$ and $n = 3, L = 2$.

What set of quantum numbers matches the orbital shown in the picture?

Solve the radial part of the Schrödinger equation for the hydrogen atom for different values of the angular momentum quantum number, $l$.

Solve the Schrödinger equation for the hydrogen atom by separating it into radial and angular parts. Given the radial equation: $\dfrac{1}{r} \dfrac{d}{dr} \left(r^2 \dfrac{dR}{dr}\right) + \left( E - \dfrac{Z^2 e^2}{4 \pi \epsilon_0 r} \right)R = 0$ and the angular equation: $\dfrac{1}{Y} \dfrac{1}{\sin \theta} \dfrac{d}{d \theta} \left( \sin \theta \dfrac{dY}{d \theta} \right) + \dfrac{1}{Y \sin^2 \theta} \dfrac{d^2 Y}{d \phi^2} = \alpha$, find the solutions for the functions $R(r)$ and $Y(\theta, \phi)$.

Determine the four quantum numbers (n, l, ml, ms) for the last valence electron of fluorine, which is the 2p^5 electron.

Find the four quantum numbers (n, l, ml, ms) for the last electron of iron, which is the 3d^6 electron.

Determine the four quantum numbers (n, l, ml, ms) for the fifth electron in the 4f subshell.

Write the orbital diagram and electron configuration for nitrogen, which has an atomic number of 7.

Using orbital diagrams, determine whether magnesium (atomic number 12) is paramagnetic or diamagnetic.

Fill the orbital diagram for phosphorus, which has 15 electrons.

Draw the orbital diagram of a sulfide ion (S²⁻), considering an atomic number of 16 for sulfur.

Draw the orbital diagram for the aluminum plus three cation (Al³⁺).

Draw the orbital diagram for the cobalt plus two ion (Co²⁺), considering transition metal ion rules.