Chemistry Practice Problems Quantum Numbers Practice Problems Solution: Part A. What is the only possible value of mℓ for ...

Solution: Part A. What is the only possible value of mℓ for an electron in an s orbital? Express your answer numerically.Part B. What are the possible values of mℓ for an electron in a d orbital? Express your answer numerically with sequential values separated by commas.Part C. Which of the following set of quantum numbers (ordered n, ℓ, mℓ, ms) are possible for an electron in an atom? Check all that apply.a. 3, 2, 0, -1/2b. -4, 3, 1, 1/2c. 3, 2, 2, -1/2d. 5, 3, -3, 1/2e. 3, 1, -2, -1/2f. 3, 3, 1, -1/2g. 2, 1, 0, -1h. 4, 2, 3, -1/2

Problem

Part A. What is the only possible value of mℓ for an electron in an s orbital? Express your answer numerically.

Part B. What are the possible values of mℓ for an electron in a d orbital? Express your answer numerically with sequential values separated by commas.

Part C. Which of the following set of quantum numbers (ordered n, ℓ, mℓ, ms) are possible for an electron in an atom? Check all that apply.

a. 3, 2, 0, -1/2
b. -4, 3, 1, 1/2
c. 3, 2, 2, -1/2
d. 5, 3, -3, 1/2
e. 3, 1, -2, -1/2
f. 3, 3, 1, -1/2
g. 2, 1, 0, -1
h. 4, 2, 3, -1/2

Solution

We're asked to answer 3 parts of the problem. Part A asks the only possible values of ml for an electron in an s orbital, part B asks the possible values of m for an electron in a d orbital, and part C asks to check all applying sets of quantum numbers that apply for an electron in an atom.


Recall that the quantum numbers that define an electron are:

• Principal Quantum Number (n): deals with the size and energy of the atomic orbital. The possible values for n are 1 to ∞.

• Angular Momentum Quantum Number (l): deals with the shape of the atomic orbital. The possible values for l are 0 to n – 1.

• Magnetic Quantum Number (ml): deals with the orientation of the atomic orbital in 3D space. The possible values for ml are the range of –l to +l.

• Spin Quantum Number (ms): deals with the spin of the electron. The possible values for ms are either –1/2 (spin down) or +1/2 (spin up).


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