Che"mystery"

I have a doubt regarding negligence of the orbital angular momentum as part of the total angular momentum of an electron while considering the 3d-series of transition metals the periodic table.

A lot of books state that for the first series (3d) of transition metals, the contribution of orbital angular momentum is of no significance and the "spin-only" angular momentum is the only contributor to the total angular momentum of an electron but fail to state why.

Could anyone kindly explain?

#Chemistry

Easy Math Editor

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Comments

The quantity "orbital angular momentum" (l), describes the properties of a single electron in an orbital. When the d shell (or even p shell) is being filled with electrons the quantum number l cannot describe this multi-electron system. To over come this the "Total angular momentum" (j) is brought into picture, j can assume values between (l - s) and (l + s). Hence the Total angular momentum of any multi-electron system confined in a specific orbital no longer depends on l, rather it depends on the value of s. Remember that s is not confined to 0.5 or -0.5, it is a quantity associated with all the electrons in the orbital.

Vitthal Yellambalse - 4 years, 3 months ago

But does the orbital angular momentum (l) affect the total angular momentum for the other transition metals (2nd and 3rd series) , Example: Tungsten ?

Nishanth Subramanian - 4 years, 3 months ago

Whatever the principle quantum number may be, the total angular momentum, j, will not change. So for tungsten, 5d series, l = 2 and 4 electrons in the d shell. So the total angular momentum will be $\frac{h\sqrt{j(j+2)}}{2\pi}$ where j is an integer between 3 and 6. This a only one case of electron arrangements.

Vitthal Yellambalse - 4 years, 3 months ago

@Vitthal Yellambalse – Thanks a lot!

Nishanth Subramanian - 4 years, 3 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$