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.

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

To determine which set of quantum numbers are possible for an electron in an atom, we need to consider the rules for assigning quantum numbers.

The quantum numbers have the following restrictions:

1. The principal quantum number (n) can take positive integer values (1, 2, 3, ...).
2. The azimuthal quantum number (ℓ) can take integer values between 0 and (n-1).
3. The magnetic quantum number (mℓ) can take integer values between -ℓ and ℓ (inclusive).
4. The spin quantum number (ms) can only be either +1/2 or -1/2.

Now, let's check each set of quantum numbers:

-4, 3, 1, 1/2: The principal quantum number (n) cannot be negative. Therefore, this set is not possible.

2, 1, -2, 1/2: The magnetic quantum number (mℓ) cannot be smaller than -ℓ. In this case, -2 is smaller than 1, so this set is not possible.

4, 2, 1, -1/2: This set follows all the restrictions, so it is possible.

4, 2, -1, -1/2: This set follows all the restrictions, so it is possible.

2, 4, 1, -1/2: The azimuthal quantum number (ℓ) cannot be larger than (n-1). In this case, 4 is larger than (2-1), so this set is not possible.

5, 3, -3, 1/2: The magnetic quantum number (mℓ) cannot be larger than ℓ. In this case, -3 is larger than 3, so this set is not possible.

5, 3, 4, 1/2: The magnetic quantum number (mℓ) cannot be larger than ℓ. In this case, 4 is larger than 3, so this set is not possible.

3, 2, 0, -2: The spin quantum number (ms) can only be either +1/2 or -1/2. In this case, -2 is not a valid value for ms, so this set is not possible.

Therefore, the possible sets of quantum numbers are:
4, 2, 1, -1/2
4, 2, -1, -1/2

To determine the possible set of quantum numbers for an electron in an atom, we need to consider the restrictions imposed by each quantum number.

The principal quantum number (n) represents the energy level or shell of the electron. It can take positive integer values (1, 2, 3, etc.). Therefore, the first and last options (-4, 3, 1, 1/2 and 5, 3, 4, 1/2) are not possible.

The azimuthal quantum number (ℓ) represents the angular momentum or subshell of the electron. It ranges from 0 to (n-1) for a given n. So, in the second option (2, 1, -2, 1/2), the value of ℓ (-2) is not within the allowed range for n=2. Similarly, in the fifth option (2, 4, 1, -1/2), the value of ℓ (4) is greater than (n-1) for n=2. Therefore, these options are not possible.

The magnetic quantum number (mℓ) represents the orientation of the subshell. It can take values from -ℓ to +ℓ, including 0. For the remaining options, let's check the values of mℓ:
- In the third option (4, 2, 1, -1/2), mℓ = 1, which is within the allowed range for ℓ=2.
- In the fourth option (4, 2, -1, -1/2), mℓ = -1, which is also within the allowed range for ℓ=2.
- In the sixth option (5, 3, -3, 1/2), mℓ = -3, which is within the allowed range for ℓ=3.
- In the last option (3, 2, 0, -2), mℓ = 0, which is within the allowed range for ℓ=2.

Therefore, the possible set of quantum numbers is:
- 4, 2, 1, -1/2
- 4, 2, -1, -1/2
- 5, 3, -3, 1/2
- 3, 2, 0, -2

These options satisfy the restrictions for the principal, azimuthal, magnetic, and spin quantum numbers.

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

n can be any positive integer.

l can be any integer from 0 to n-1
ml can be -l to +l in steps of 1
ms can be either +1/2 or -1/2

1 is no because n can't be negative.
2 is no because ml can be -1,0,or +1 but not 2.
3 is OK.
You go through the others.