Hydrogen Atom: Quantum States, Angular Momentum, and Probability

All flashcards

Fixed-proton approximation

Treating the proton as stationary because it is much more massive than the electron.

Hydrogen Coulomb potential energy

With zero energy at infinite separation, $U(r)=-ke^2/r$.

Hydrogen energy-level degeneracy

In this model, states with the same $n$ but different allowed $l$ and $m$ have the same energy.

Orbital angular momentum magnitude

For quantum number $l$, the magnitude is $L=\sqrt{l(l+1)}\hbar$.

Atomic orbital

A region of space enclosing a chosen fraction of an electron’s probability, often about 90%.

Quiz questions

1. For orbital quantum number $l=2$, which set contains all allowed values of $m$?Answer: $-2,-1,0,1,2$
2. What is the energy of a hydrogen state with principal quantum number $n=2$?Answer: $-3.4\,\text{eV}$
3. For a state with magnetic quantum number $m$, what is the $z$-component of orbital angular momentum?Answer: $L_z=m\hbar$
4. In the hydrogen ground state, at what radial distance is the radial probability density greatest?Answer: At the Bohr radius, $a_0$.
5. What does $|\psi|^2$ represent in quantum mechanics?Answer: Probability density for finding the particle at a position.