Question

THE WAVE FUNCTION FOR THE HYDROGEN ATOM DEPENDS UPON THREE QUANTUM NUMBERS N,L AND M. NAME THESE QUANTUM NUMBERS.

Answer 1

Answer on Question #37531 – Physics - Quantum Mechanics

Question: the wave function for the hydrogen atom depends upon three quantum numbers $n, l, m$. Name these quantum numbers.

Answer:

1) $n$ ($n = 1,2,3\ldots$) is the total quantum number, which arises from the solution of the radial part of the Schrödinger equation for the hydrogen atom. It determines the possible values of the energy for the electron in the hydrogen atom $E_{n} = -\frac{13,6}{n^{2}} eV$.

2) $l$ ($l = 0,1,\ldots,n-1$) is the orbital quantum number, which determines the magnitude of the orbital angular momentum $L^2 = \hbar^2 l(l + 1)$.

3) $m$ ($m = -l, -l + 1, \ldots, l-1, l$) is the magnetic quantum number, that comes from the azimuthal equation of the hydrogen Schrödinger equation. It determines the possible values of the $z$-component of the angular momentum $L_z = m\hbar$.