Question

What will be the degeneracy for n=4 for hydrogen atom

Answer 1

2n²  = 2 x (4)² = 32

For the n=4 state we have

n=4, l=3, ml = 3, ms = ±1 / 2

n=4, l=3, ml = 2, ms = ±1 / 2

n=4, l=3, ml = 1, ms = ±1 / 2

n=4, l=3, ml = 0, ms = ±1 / 2

n=4, l=3, ml = −1, ms = ±1 / 2

n=4, l=3, ml = −2, ms = ±1 / 2

n=4, l=3, ml = −3, ms = ±1 / 2

n=4, l=2, ml = 2, ms = ±1 / 2

n=4, l=2, ml = 1, ms = ±1 / 2

n=4, l=2, ml = 0, ms = ±1 / 2

n=4, l=2, ml = −1, ms = ±1 / 2

n=4, l=2, ml = −2, ms = ±1 / 2

n=4, l=1, ml = 1, ms = ±1 / 2

n=4, l=1, ml = 1, ms = ±1 / 2

n=4, l=1, ml = 0, ms = ±1 / 2

n=4, l=1, ml = 0, ms = ±1 / 2

n=4, l=0, ml = 0, ms = ±1 / 2

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