Question

List the quantam numbers for all possible electron states in the hydrogem atom with principal quantam number n = 3.

Answer 1

all possible electron states in the hydrogem atom with principal quantam number n = 3

Angular Momentum (Secondary, Azimunthal) Quantum Number (l):  l = 0, ..., n-1

so, l = 0,1,2

Magnetic Quantum Number (m_l):  m_l = -l, ..., 0, ..., +l

for l=0 --------> ml = 0

for l=1 -------> ml = -1, 0, 1

for l=2 -----> ml = -2, -1, 0, 1, 2

so, ml = -2, -1, 0, +1 , +2

Spin Quantum Number (m_s):  m_s = +½ or -½

for each ml one up and one down spin