Question

What is the angular momentum of a particle in the l = 5 state? What are the allowed values of the z component of the angular momentum? Sketch the possibilities.

Answer 1

(2)

Solution: The magnitude of angular momentum L of a particle in the l = 5 state is given by,

L = √[l*(l + 1)]*ђ where ђ = h/2π h being Planck’s constant.

L = √30*ђ

L = √[5*(5 + 1)]*(6.626*10^-34 J.s)/(2*3.1416)

L = 5.7761*^-34 J.s

Thus the answer is, angular momentum L = √30*ђ or L = 5.7761*^-34 J.s

For a orbital number l, the associated orbital magnetic numbers are 0, 0, +1, +2, +3,……., +l.

For l = 5, the orbital magnetic numbers are m_l = 0, +1, +2, +3, +4, +5 that is, m_l = -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

The allowed values of the z component of the angular momentum L_z are given by,

L_z = m_l*ђ

-5ђ, -4ђ, -3 ђ, -2 ђ, -1 ђ, 0, 1 ђ, 2 ђ, 3 ђ, 4 ђ and 5 ђ.

The possibilities can be sketched as