Chemistry Practice Problems Introduction to Quantum Mechanics Practice Problems Solution: An electron in a 3d orbital could have which of th...

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Solution: An electron in a 3d orbital could have which of the following quantum numbers?1. n = 3; ℓ = 3; m ℓ = 12. n = 3; ℓ = 1; m ℓ = -13. n = 3; ℓ= 2; m ℓ = 04. n =3; ℓ = 0; m ℓ = 05. n = 3; ℓ = 1; m ℓ = 26. n = 3; ℓ = 2; m ℓ = -37. n = 2; ℓ = 2; m ℓ = 6

Problem

An electron in a 3d orbital could have which of the following quantum numbers?

1. n = 3; ℓ = 3; m ℓ = 1

2. n = 3; ℓ = 1; m ℓ = -1

3. n = 3; ℓ= 2; m ℓ = 0

4. n =3; ℓ = 0; m ℓ = 0

5. n = 3; ℓ = 1; m  = 2

6. n = 3; ℓ = 2; m ℓ = -3

7. n = 2; ℓ = 2; m ℓ = 6

Solution

To determine which quantum numbers will correspond to an electron in a 3d orbital, let’s first define the values of first three quantum numbers:

 principal quantum number (n)  energy level in orbitals and its value could be any positive integer starting from 1

 angular momentum quantum number (ℓ)  (l) has to be at least 1 less than n, range of values from 0 up to (n-1) and each number corresponds to a subshell:

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