What is the total number of orbitals having n = 5 and ℓ = 3?
A. 3
B. 5
C. 7
D. 9
E. 10
To find the total number of orbitals with specific quantum numbers, you need to know the angular momentum quantum number (ℓ) and the principal quantum number (n). The relationship between these two quantum numbers is given by the equation:
Number of orbitals = 2 * (2ℓ + 1)
In this case, ℓ = 3 and n = 5. Substituting these values into the equation, we can find the number of orbitals:
Number of orbitals = 2 * (2ℓ + 1)
= 2 * (2*3 + 1)
= 2 * (6 + 1)
= 2 * 7
= 14
Therefore, the total number of orbitals with n = 5 and ℓ = 3 is 14.
None of the options A, B, C, D, and E match the correct answer.