The quantum mechanical model of the hydrogen atom requires that if the principal quantum number = 5,there will be how many permitted orbital quantum numbers?
A)3
B)5
C)10
D)25

Question

Quizplus · Accepted Answer

The number of permitted orbital quantum numbers for a given principal quantum number is equal to n^2. Therefore, for n=5, there will be 5^2=25 permitted orbital quantum numbers. However, only 5 of these will be unique since each value of l can have 2(l)+1 values of m, where m is the magnetic quantum number ranging from -l to +l. So the number of permitted orbitals is given by the formula 2(l)+1. For n=5, the possible values of l are 0, 1, 2, 3, and 4, each with 2(l)+1 possible values of m. Thus, the total number of unique orbitals is 1+3+5+7+9=25.

The Quantum Mechanical Model of the Hydrogen Atom Requires That