In the quantum mechanical picture of the hydrogen atom, the orbital angular momentum of the electron may be zero in any of the possible energy states. For which energy state must the orbital angular momentum be zero?
n = 1
n = 2
n = 3
n = 4
Give your reasoning.
I am not sure about this one but I think the answer is 2 but I am unsure why. Please explain.
The key word in that question is MUST. The correct answer is 1. See my answer to your previous question.
To determine for which energy state the orbital angular momentum of the electron must be zero, we need to consider the possible values of the angular momentum quantum number, denoted by ℓ.
The angular momentum quantum number, ℓ, is related to the energy state of the hydrogen atom given by the principal quantum number, n. The values of ℓ range from 0 to (n-1), and they determine the shape of the orbitals in the atom.
To find the energy state for which the orbital angular momentum must be zero, we need to find the value of ℓ that corresponds to zero angular momentum.
For n = 1, the possible value of ℓ is 0. So, the angular momentum can be zero for this energy state.
For n = 2, the possible values of ℓ are 0 and 1. The value of ℓ = 0 corresponds to s orbital, which has spherical symmetry and no orbital angular momentum. Therefore, the angular momentum can be zero for n = 2.
For n = 3, the possible values of ℓ are 0, 1, and 2. None of these values of ℓ corresponds to zero angular momentum.
For n = 4, the possible values of ℓ are 0, 1, 2, and 3. None of these values of ℓ corresponds to zero angular momentum.
Therefore, the correct answer is n = 2, where the orbital angular momentum of the electron can be zero.