 Home

Natural science

Physics

Quantum mechanics

Schrödinger equation

Schrödinger equation solution for the hydrogen atom

Atomic orbital

This is a section about Magnetic quantum number!

Magnetic quantum number is a very important subject about which there is a lot to say.

For example, this sentence. And then another one.


Magnetic quantum number

I can't believe you got such a basic fact wrong!

1+1<svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z'/></svg>​=3, not 2 as mentioned

$\sqrt{1 + 1} = 3$, not 2 as mentioned

{title2=$m_l$}
{wiki}

Fixed <quantum angular momentum> in a given direction.

Can range between $\pm l$.

E.g. consider <gallium> which is 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1:
* the electrons in <s-orbitals> such as 1s, 2d, and 3d are $l=0$, and so the only value for $m_l$ is 0
* the electrons in <p-orbitals> such as 2p, 3p and 4p are $l=1$, and so the possible values for $m_l$ are -1, 0 and 1
* the electrons in <d-orbitals> such as 2d are $l=2$, and so the possible values for $m_l$ are -2, -1, 0 and 1 and 2

The z component of the <quantum angular momentum> is simply:
$$
L_z = m_l \hbar
$$
so e.g. again for gallium:
* <s-orbitals>: necessarily have 0 z angular momentum
* <p-orbitals>: have either 0, $- \hbar$ or $+ \hbar$ z angular momentum

Note that this direction is arbitrary, since for a fixed <azimuthal quantum number> (and therefore fixed total angular momentum), we can only know one direction for sure. $z$ is normally used by convention.

Magnetic quantum number

 Ancestors (7)

 Discussion (1)

  Latest discussions

  Top discussions

 Articles by others on the same topic (3)

Magnetic quantum number

 Ancestors (7)

 Discussion (1)  Subscribe (1)

  Latest discussions

  Top discussions

 Articles by others on the same topic (3)

 Discussion (1)