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Suppose that n ≥ 3. Prove that n² < 2?

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Final answer:

The question appears to have a typo, as n squared is not less than 2 when n is greater than or equal to 3. The explanation provided analyzes the number of subshells and orbitals in the n = 3 principal shell in Chemistry.

Step-by-step explanation:

The question seems to contain a typo, as no number n greater than or equal to 3 will result in n squared being less than 2. However, if we consider counting the subshells and orbitals in a principal shell with n = 3, which relates to Chemistry, the answer can be found using the quantum numbers.

In the n = 3 shell, there are three subshells and these are the 's', 'p', and 'd' subshells.Each subshell can hold a specific number of electrons, defined by the formula 2l+1, where l is the azimuthal quantum number associated with each subshell.

The 's' subshell (with l = 0) can hold 2 electrons, the 'p' subshell (with l = 1) can hold 6 electrons, and the 'd' subshell (with l = 2) can hold 10 electrons.Therefore, the total number of electrons that can be accommodated in the n = 3 shell is the sum of the maximum number of electrons in each subshell, which gives us 2 + 6 + 10 = 18 electrons.

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