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Chapter 7: Problem 59

List all the possible subshells and orbitals associated with the principal quantum number \(n\), if \(n=5\).

Short Answer

Expert verified
For \(n = 5\), the subshells are s, p, d, f, and g, with 1, 3, 5, 7, and 9 orbitals respectively, resulting in a total of 25 orbitals.

Step by step solution

01

List All Possible Subshells

For \(n = 5\), subshells are determined by each value of azimuthal quantum number (\(l\)) from 0 to \(n - 1\). Here, the possible values of \(l\) are 0, 1, 2, 3, and 4. These correspond to the subshells s, p, d, f, and g.
02

Calculate Orbitals for Each Subshell

The number of orbitals in a subshell is given by the formula \(2l + 1\). For s subshell (\(l = 0\)), there's 1 orbital, for p (\(l = 1\)), there are 3 orbitals, for d (\(l = 2\)), there are 5 orbitals, for f (\(l = 3\)), there are 7 orbitals, and for g (\(l = 4\)), there are 9 orbitals.
03

Present the Final Answer

So for \(n = 5\), we have 5 subshells (s, p, d, f, g) and each have 1, 3, 5, 7, 9 orbitals respectively. Therefore, there are total 25 orbitals.

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