Angular momentum in quantum mechanics (introductory)
Formalism and applications · Physics
Study notes
Let's calculate the magnitude of the orbital angular momentum for an electron in a hydrogen atom with quantum number l = 1. Step 1: Identify the formula. The magnitude L is given by L = sqrt(l(l+1)) * ħ, where ħ (h-bar) is h/2π. Step 2: Plug in the value. Here l = 1. So, L = sqrt(1(1+1)) * ħ. Step 3: Simplify. L = sqrt(2) * ħ. Step 4: Calculate numerical value. Since ħ ≈ 1.054 × 10^-34 J·s, L ≈ 1.414 * 1.054 × 10^-34 ≈ 1.49 × 10^-34 J·s. This shows the angular momentum is not l*ħ (which would be 1*ħ), but specifically sqrt(2)*ħ.