Final answer:
Zinc (Zn) has a total of 18 electrons in the n = 3 shell in its ground state, comprising 2 electrons in the 3s orbital, 6 electrons in the 3p orbitals, and 10 electrons in the 3d orbitals.
Step-by-step explanation:
In the ground state of zinc (Zn), the number of electrons occupying atomic orbitals with n = 3 is 18. Zinc's electron configuration is [Ar]4s²3d¹⁰, and while the 4s electrons are not in the n = 3 shell, all ten of the 3d electrons are, plus the eight electrons in the 3s and 3p orbitals. Here is the breakdown:
- 3s has l = 0; thus 2(2l+1) = 2(0+1) = 2
- 3p has l = 1; thus 2(2l+1) = 2(2+1) = 6
- 3d has l = 2; thus 2(2l+1) = 2(4+1) = 10
Total = 18 electrons (in the n = 3 shell). The general rule for the maximum number of electrons within a shell is 2n², which for n = 3 calculates to 2(3)² = 2(9) = 18.