How many different values of ml are possible in the 5d sublevel?

The answer is 5 but i dont know how? If it was 3d then the aswer would be 5 right? And if it was 5f it would be 7. Or am i thinking of something different?

Answer 1

Quantum numbers….

n = principle quantum number … the energy level of the electron
ℓ = azimuthal quantum number … the sublevel of the electron (s, p, d, f)
….. values range from 0 to n-1 (s=0, p=1, d=2, f=3)
mℓ = magnetic quantum number … the orbital within the sublevel
…….. values range from -ℓ…0…+ℓ
ms = spin quantum number…. the electron(s) within the orbital
…….. values are +½ and -½

Consider the 5d sublevel
n = 5
ℓ = 2 ….. values are 0 for s, 1 for p, 2 for d, 3 for f
mℓ = -ℓ…0…+ℓ …. values are -2, -1, 0, 1, 2 … now count them… 5 orbitals

Now, consider the 5f sublevel
n = 5
ℓ = 3 ….. values are 0 for s, 1 for p, 2 for d, 3 for f
mℓ = -ℓ…0…+ℓ …. values are -3, -2, -1, 0, 1, 2, 3 … now count them… 7 orbitals

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