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How many electrons in an atom could have these sets of quantum numbers?=3 =4,ℓ=3=6, ℓ=1, ℓ=−1

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In this question, we have 3 situations:

1. electrons n=3, this means that the electrons belong to the 3rd shell in an atom, so the electron configuration of this atom could be up to: 3s2 3p6 3d10, and each of these numbers after the letter (orbitals) represents number of electrons, therefore if we sum all these numbers, 2+6+10 = 18 electrons, so 18 electrons could have this n=3 quantum number.

18 electrons

2. In this case we have n=4 and l=3, again n is the shell number, so these electrons are located in the 4th shell of the atom, but l=3 means that these electrons are in the last possible orbital, the "f" orbital, since the 4th period has 4 orbitals (s,p,d, and f), l=3 represents the f orbital, and this orbital can have up to 14 electrons

14 electrons

3. In this case we have n=6, l=1, ml=-1, n again representing the shell value, and l representing the orbital value, l=1 means that we have the "p" orbital, an orbital that usually can hold up to 6 electrons, but ml=-1 represents just 1 part of the orbital p, and each suborbital can hold up to 2 electrons.

2 electrons

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