Question

Give the value of the quantum number ℓ, if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of 6√(h/2π).

Answer 1

The value of the quantum number ℓ for a hydrogen atom with an orbital angular momentum of 6√(h/2π) is 2.

Step-by-step explanation:

The value of the quantum number ℓ for a hydrogen atom with an orbital angular momentum of 6√(h/2π) can be determined using the formula L = √(ℓ(ℓ+1))ħ, where L is the magnitude of the orbital angular momentum. Rearranging the formula, we get ℓ(ℓ+1) = (L/ħ)^2. Substituting the given value of L, we have ℓ(ℓ+1) = (6√(h/2π)/ħ)^2. Solving for ℓ, we find that ℓ = 2.