Recall that degeneracy is a count of all the different combinations of quantum numbers in a wavefunction that would result in the same energy. When we first described the hydrogen atom, we described it as a three-dimensional problem, so we said there were three quantum numbers. However, there is a fourth dimension that we just described in this unit, spin. So we've added a fourth quantum number. They are as follows: n, I, mj and mg. Write out all the possible combinations for quantum numbers for the following three scenarios: n = 1, n = 2 and n = 3. Count up all the possible combinations for each scenario and use the result to determine a general formula for the degeneracy. The general formula for degeneracy is. O 2n2 n2 O 2n+1 O n-1 O O O

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Recall that degeneracy is a count of all the different combinations of quantum numbers in a wavefunction that would result in the same energy. When
we first described the hydrogen atom, we described it as a three-dimensional problem, so we said there were three quantum numbers. However, there
is a fourth dimension that we just described in this unit, spin. So we've added a fourth quantum number. They are as follows: n, I, mj and mg. Write out
all the possible combinations for quantum numbers for the following three scenarios: n = 1, n = 2 and n = 3. Count up all the possible combinations for
each scenario and use the result to determine a general formula for the degeneracy. The general formula for degeneracy is.
O 2n2
n2
O 2n+1
O n-1
O O O
Transcribed Image Text:Recall that degeneracy is a count of all the different combinations of quantum numbers in a wavefunction that would result in the same energy. When we first described the hydrogen atom, we described it as a three-dimensional problem, so we said there were three quantum numbers. However, there is a fourth dimension that we just described in this unit, spin. So we've added a fourth quantum number. They are as follows: n, I, mj and mg. Write out all the possible combinations for quantum numbers for the following three scenarios: n = 1, n = 2 and n = 3. Count up all the possible combinations for each scenario and use the result to determine a general formula for the degeneracy. The general formula for degeneracy is. O 2n2 n2 O 2n+1 O n-1 O O O
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