An electron in an atom is in a state with ℓ=3 and m_ℓ =2.The angle between and the z axis is: A)30$\degree$ B)35.3$\degree$ C)48.2$\degree$ D)54.7$\degree$ E)60$\degree$

Question

Quizplus · Accepted Answer

The angle θ between the angular momentum vector and the z-axis is given by cos(θ) = mℓ/√(ℓ(ℓ+1)). For ℓ=3 and mℓ=2, cos(θ) = 2/√(3(3+1)) = 2/√12 = 1/√3. Therefore, θ = cos^(-1)(1/√3) ≈ 54.7°.

An Electron in an Atom Is in a State with ℓ=3