Chemistry Practice Problems Quantum Numbers Practice Problems Solution: How many different orbitals can have the principal...

Solution: How many different orbitals can have the principal quantum number n = 3?(a) 9 (b) 4 (c) 6 (d) 5 (e) 18

Problem

How many different orbitals can have the principal quantum number n = 3?

(a) 9 

(b) 4 

(c) 6 

(d) 5 

(e) 18

Solution

We’re being asked which of the following combinations could give the quantum numbers for the single valence electron of the copper in its ground state.

Recall that the quantum numbers are:

principal quantum number (n)  energy level in orbitals and its value could be any positive integer starting from 1 to infinity.
angular momentum quantum number (ℓ) → (l) has to be at least 1 less than n, range of values from 0 up to (n-1)

▪ Each ℓ value corresponds to a subshell:

 = 0 → s subshell
 = 1 → p subshell 
 = 2 → d subshell
 = 3 → f subshell

• magnetic quantum number (m) → range of values from - to + 

▪ The m values (for each ℓ) represent an orbital for the subshell:

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