The principle quantum number for the electron in a hydrogen atom is n = 5. According to the quantum mechanical picture of the atom, what is the maximum possible value for the magnitude of the z-component of the angular momentum of the electron? A)3.17 × 10^-³⁴ kg .m²/s B)4.22 × 10^-³⁴ kg . m²/s C)1.99 × 10^-³⁴ kg . m²/s D)1.06 × 10^-³⁴ kg . m²/s E)2.11 × 10^-³³ kg . m²/s

Question

Quizplus · Accepted Answer

The maximum value of the z-component of angular momentum is given by m_l * ħ, where m_l is the magnetic quantum number and can take values from -l to +l. For n=5, the maximum l is 4, so the maximum m_l is also 4. Therefore, the maximum magnitude is 4ħ = 4 * 1.0545718 × 10^-34 kg.m^2/s = 4.22 × 10^-34 kg.m^2/s.

The Principle Quantum Number for the Electron in a Hydrogen