Question

which orbital diagram has the correct placement for 21 electrons.
○ 3d↑ _ _ _ _
3p↑↓↑↓↑↓
2p↑↓↑↓↑↓
4s↑↓
3s↑↓
2s↑↓
1s↑↓
○ 3d↑ ↑ ↑ _ _
3p↑↓↑↓↑↓
3s↑↓
2p↑↓↑↓↑↓
2s↑↓
1s↑↓
○ 3d↑ _ _ _ _
4s↑↓
3p↑↓↑↓↑↓
3s↑↓
2p↑↓↑↓↑↓
2s↑↓
1s↑↓
○ 3d↑ ↑ ↑ _ _
3p↑↓↑↓↑↓
2p↑↓↑↓↑↓
3s↑↓
2s↑↓
1s↑↓

Explanation:

Step1: Recall electron - filling rules

Electrons fill orbitals according to the Aufbau principle (fill lower - energy orbitals first), Pauli exclusion principle (each orbital can hold a maximum of 2 electrons with opposite spins), and Hund's rule (for degenerate orbitals, electrons fill them singly first with parallel spins). The order of filling is \(1s<2s < 2p<3s<3p<4s<3d\).

Step2: Calculate electrons in each orbital

• \(1s\) orbital holds 2 electrons (\(\uparrow\downarrow\)).
• \(2s\) orbital holds 2 electrons (\(\uparrow\downarrow\)).
• \(2p\) has 3 orbitals and holds 6 electrons (\(\uparrow\downarrow\)\(\uparrow\downarrow\)\(\uparrow\downarrow\)).
• \(3s\) orbital holds 2 electrons (\(\uparrow\downarrow\)).
• \(3p\) has 3 orbitals and holds 6 electrons (\(\uparrow\downarrow\)\(\uparrow\downarrow\)\(\uparrow\downarrow\)).
• \(4s\) orbital holds 2 electrons (\(\uparrow\downarrow\)). So far, \(2 + 2+6 + 2+6 + 2=20\) electrons.
• The 21st electron goes into the \(3d\) orbital. According to Hund's rule, in the \(3d\) sub - level (which has 5 degenerate orbitals), the first electron in \(3d\) will occupy an empty orbital with a spin - up (\(\uparrow\)).

Answer:

The second option (where \(3d\) has one electron with spin - up, \(4s\) is filled with 2 electrons, \(3p\) is filled with 6 electrons, \(3s\) is filled with 2 electrons, \(2p\) is filled with 6 electrons, \(2s\) is filled with 2 electrons, and \(1s\) is filled with 2 electrons) has the correct placement for 21 electrons.