How many orbitals are found in the d sublevel?

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How many orbitals are found in the d sublevel?

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Answer 1 · 2015-12-03T04:52:51

We can derive this from knowing that the atomic orbitals each exist in accordance with angular momentum quantum number $l$ $l$ .

Recall how $l$ $l$ tells you the shape of the atomic orbital. That just means:

$l = 0 \to s$ $l = 0 -> s$ orbital
$l = 1 \to p$ $l = 1 -> p$ orbital
$l = 2 \to d$ $l = 2 -> d$ orbital
etc.

Additionally, what we have associated with $l$ $l$ is the magnetic quantum number $m_{l}$ $m_l$ , the projection of $l$ $l$ in the negative, unsigned, and positive directions. In other words...

$m_{l} = 0, \pm 1, \pm 2, . . . \pm (l - 1), \pm l$ $m_l = 0, pm 1, pm 2, . . . pm (l-1), pm l$

If $l = 2$ $l = 2$ , then:

$m_{l} = - 2, - 1, 0, + 1, + 2$ $color(blue)(m_l = -2, -1, 0, +1, +2)$

Each individual $m_{l}$ $m_l$ value corresponds to a unique orbital.

That indicates that five orbitals are available in the $d$ $d$ orbitals. Specifically, the $d_{z^{2}}^{2}$ $d_(z^2)$ , $d_{x^{2} - y^{2}}^{2}$ $d_(x^2 - y^2)$ , $d_{x y}$ $d_(xy)$ , $d_{x z}$ $d_(xz)$ , and $d_{y z}$ $d_(yz)$ orbitals.

Furthermore, from knowing that the spin quantum number $m_{s}$ $m_s$ for an electron is $\pm 1/2$ $pm"1/2"$ (two spin states), and recalling the Pauli exclusion principle (two electrons in one orbital must be opposite spins), there can be a max of two electrons per orbital.

Therefore, the total number of electrons in five orbitals can be a maximum of 10.

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How many orbitals are found in the d sublevel?

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