Question

question 12 (1 point)
how many orbitals in the n = 3 energy level?
25
16
9
4
1

Explanation:

Step1: Determine the possible values of \( l \)

For a given \( n \), \( l = 0,1,\cdots,n - 1 \). When \( n=3 \), \( l = 0,1,2 \).

Step2: Calculate the number of orbitals for each \( l \)

• When \( l = 0 \) (s - orbital), the number of orbitals is \( 2l+1=1 \).
• When \( l = 1 \) (p - orbitals), the number of orbitals is \( 2l + 1=3 \).
• When \( l = 2 \) (d - orbitals), the number of orbitals is \( 2l+1 = 5 \).

Step3: Sum up the number of orbitals

The total number of orbitals is \( \sum_{l = 0}^{n - 1}(2l + 1) \). Substituting \( n = 3 \), we have \( 1+3+5=9 \). Another formula is \( n^{2} \), when \( n = 3 \), \( n^{2}=9 \).

Answer:

9