Indicate which of the following quantum numbers are unacceptable:

(a)(1,2,0,1/2) (b) (3,2,0,1/2) (c)(3,2,2,1) (d) (4,3,2,-1/2)

a and c are not acceptable.

a. n = 1
l can be 0 and only 0 which makes 2 no go.
c. n = 3
l can be 0, 1, or 2 which is ok at 2
ml can be -2,-1,0,1,2 so 2 is ok.
ms can be +1/2 or -1/2 so 1 is not ok.

To determine if a set of quantum numbers is acceptable, we need to check if they follow the rules defined by the quantum theory. The four quantum numbers are:

1. Principal quantum number (n): Represents the energy level or the size of the orbital.
2. Azimuthal quantum number (l): Determines the shape of the orbital and ranges from 0 to (n-1).
3. Magnetic quantum number (m_l): Specifies the orientation of the orbital within a subshell and ranges from -l to +l.
4. Spin quantum number (m_s): Represents the spin of the electron and can have values of +1/2 (up spin) or -1/2 (down spin).

Now let's check each set of quantum numbers:

(a) (1, 2, 0, 1/2):
- n = 1, l = 2, m_l = 0, m_s = 1/2
This set is acceptable as the principal quantum number (1) and the azimuthal quantum number (2) are within an acceptable range.

(b) (3, 2, 0, 1/2):
- n = 3, l = 2, m_l = 0, m_s = 1/2
This set is also acceptable as all the quantum numbers fall within the acceptable range.

(c) (3, 2, 2, 1):
- n = 3, l = 2, m_l = 2, m_s = 1
The magnetic quantum number (m_l) cannot be greater than the azimuthal quantum number (l). Therefore, this set is unacceptable.

(d) (4, 3, 2, -1/2):
- n = 4, l = 3, m_l = 2, m_s = -1/2
This set is acceptable as none of the quantum numbers violate the rules.

In summary, the unacceptable set of quantum numbers is (c) (3, 2, 2, 1).

To determine which of the given quantum numbers are unacceptable, we need to consider the rules for each quantum number.

(a) (1,2,0,1/2):
The first quantum number, n, represents the principal energy level. It can have any positive integer value. Therefore, (1) is acceptable.

The second quantum number, l, represents the orbital angular momentum. It can have integer values ranging from 0 to n-1. Since n is 1, l can only be 0. Therefore, (2) is acceptable.

The third quantum number, ml, represents the magnetic quantum number. It can have integer values ranging from -l to +l. Since l is 0, ml can only be 0. Therefore, (0) is acceptable.

The fourth quantum number, ms, represents the spin quantum number. It can have two possible values, +1/2 or -1/2. Therefore, (1/2) is acceptable.

Therefore, (a) is an acceptable set of quantum numbers.

(b) (3,2,0,1/2):
Similar to (a), the values of the quantum numbers n, l, and ml are within the acceptable range.

Therefore, (b) is an acceptable set of quantum numbers.

(c) (3,2,2,1):
The value of the third quantum number, ml, cannot be greater than l. Here, ml is 2, while l is 2. Therefore, (c) is an unacceptable set of quantum numbers.

(d) (4,3,2,-1/2):
Similar to (c), the value of the third quantum number, ml, cannot be greater than l. Here, ml is 2, while l is 3. Therefore, (d) is an unacceptable set of quantum numbers.

In summary, the unacceptable quantum numbers are:

(c) (3,2,2,1)
(d) (4,3,2,-1/2)