Question

Learning Goal:

To learn the restrictions on each quantum number.

Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers.

The principal quantum number n corresponds to the shell in which the electron is located. Thusn can therefore be any integer. For example, an electron in the 2p subshell has a principal quantum number of n=2 because 2p is in the second shell.

The azimuthal or angular momentum quantum number ? corresponds to the subshell in which the electron is located. s subshells are coded as 0, p subshells as 1, d as 2, and f as 3. For example, an electron in the 2p subshell has ?=1. As a rule, ? can have integer values ranging from 0 to n?1.

The magnetic quantum number m?corresponds to the orbital in which the electron is located. Instead of 2px, 2py, and 2pz, the three 2p orbitals can be labeled ?1, 0, and 1, but not necessarily respectively. As a rule, m?can have integer values ranging from ?? to +?.

The spin quantum number ms corresponds to the spin of the electron in the orbital. A value of 1/2 means an "up" spin, whereas ?1/2 means a "down" spin.

Part A

What is the only possible value of m? for an electron in an s orbital?

Express your answer numerically.

Part B

What are the possible values of m? 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, ?, m?, ms) are possible for an electron in an atom?

Check all that apply.

4, 2, 3, -1/2
-4, 3, 1, 1/2
3, 2, 0, -2
4, 2, -2, 1/2
2, 1, 0, 1/2
3, 4, 0, 1/2
5, 3, 0, 1/2
2, 1, -2, 1/2

Answer 1

The magnetic quantum number for an electron in an s orbital is 0. For a d orbital, the magnetic quantum numbers range from -2 to 2. The possible quantum number sets for an electron include combinations that adhere to the specific rules of quantum numbers.

Step-by-step explanation:

Quantum numbers are essential in describing the state of electrons in an atom. Understanding the restrictions on each is crucial for comprehending the electronic structure of an atom.

Part A

The only possible value of the magnetic quantum number (ml) for an electron in an s orbital is 0.

Part B

For an electron in a d orbital, the possible values of ml are -2, -1, 0, 1, 2.

Part C

Examining the set of quantum numbers for an electron, possible combinations must abide by the restrictions of n (principal quantum number), l (azimuthal quantum number), ml (magnetic quantum number), and ms (spin quantum number).

The following sets are possible for an electron:

4, 2, 3, -1/2 (Incorrect: ml cannot be 3 for l=2)

-4, 3, 1, 1/2 (Incorrect: n must be a positive integer)

3, 2, 0, -2 (Incorrect: ms must be ±1/2)

4, 2, -2, 1/2

2, 1, 0, 1/2

3, 4, 0, 1/2 (Incorrect: l must be less than n)

5, 3, 0, 1/2

2, 1, -2, 1/2 (Incorrect: ml cannot be -2 for l=1)

Answer 2

it 3

Step-by-step explanation: