Question

What is the maximum angular momentum Lmax that an electron with principal quantum number n = 2 can have? Express your answer in units of ℏ.

Answer 1

Answer:

$L_{max} = 1.414$ ℏ

Given:

Principle quantum number, n = 2

Solution:

To calculate the maximum angular momentum, $L_{max}$, we have:

$L_{max} = \sqrt {l(1 + l)}$                              (1)

where,

l = azimuthal quantum number or angular momentum quantum number

Also,

n = 1 + l

2 = 1 + l

l = 1

Now,

Using the value of l = 1 in eqn (1), we get:

$L_{max} = \sqrt {1(1 + 1)} = \sqrt 2$

$L_{max} = 1.414$ ℏ