Question

Indicate which of the following sets of quantum numbers could not occur and explain why:

(A) 1,1,0, 1/2
(B) 2,1,0, 1/2
(C) 2,0,1, 1/2
(D) 2,1,0,0
(E) 3,2,0, 1/2

Answer 1

The validity of a set of quantum numbers depends on adherence to certain rules. Set (A) and Set (C) are not allowed because they violate the rules for the azimuthal and magnetic quantum numbers, respectively. Set (D) is also not allowed because the spin quantum number is incorrect.

Step-by-step explanation:

The student is asking about the validity of different sets of quantum numbers. Quantum numbers are used to describe the properties of electrons in atoms. The four quantum numbers are: the principal quantum number (n), the azimuthal (or angular momentum) quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).

Here are the rules that must be followed for the quantum numbers to be valid:

• The principal quantum number n must be a positive integer (n > 0).
• The azimuthal quantum number l can take on any integer value from 0 to n-1.
• The magnetic quantum number ml can take on integer values between -l and +l, including zero.
• The spin quantum number ms can only be +1/2 or -1/2.

From the options given by the student:

• Set (A) 1,1,0, 1/2 is not allowed because l cannot be equal to n.
• Set (B) 2,1,0, 1/2 is allowed.
• Set (C) 2,0,1, 1/2 is not allowed because ml must be between -l and +l, and here ml does not fall in the correct range (should be -0 to 0).
• Set (D) 2,1,0,0 is not allowed because the spin quantum number must be ±1/2, not 0.
• Set (E) 3,2,0, 1/2 is allowed.