Final answer:
Electrons within an atom are arranged into shells and subshells, with the number of electrons in a shell given by 2n² and that in each subshell by 2(2l+1). In the case of the n=3 shell, these formulas give 2, 6, and 10 electrons in the 3s, 3p, and 3d subshells respectively, totaling 18 electrons, which confirms the 2n² rule.
Step-by-step explanation:
The student's question pertains to the quantum mechanical model of the atom, specifically about the distribution of electrons in atomic orbitals. According to the model, the electron configuration within an atom is organized into shells and subshells. The number of electrons that can occupy a shell is given by the formula 2n², where 'n' is the principal quantum number of the shell.
The number of electrons that can be in each subshell is given by 2(2l+1), where 'l' is the azimuthal quantum number, or also known as the angular momentum quantum number, corresponding to the subshell.
For example, in the n=3 shell:
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- 3s subshell (l=0), we have 2(2×0+1) = 2 electrons
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- 3p subshell (l=1), we have 2(2×1+1) = 6 electrons
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- 3d subshell (l=2), we have 2(2×2+1) = 10 electrons
Adding these up, the total number of electrons in the n=3 shell is 2+6+10 = 18 electrons, which matches the formula 2n², since 2(3)² = 2(9) = 18.