Question

Which of the following sets of quantum numbers is not possible? (Choose all that are not possible) (Note: If you have not learned about ms yet, it can have values of either +1/2 or -1/2. Each of the choices here has a valid value of ms.)

A. n = 8, l = 5, ml = -5, ms = -1/2
B. n = 4, l = 0, ml = 0, ms = -1/2
C. n = 1, l = 0, ml = 0, ms = -1/2
D.n = 1, l = 2, ml = 0, ms = +1/2
E. n = 3, l = 2, ml = 3, ms = +1/2
F.n = 5, l = -4, ml = 3, ms = -1/2
G.n = 4, l = 4, ml = 4, ms = -1/2

Answer 1

Sets D, E, and F are not possible quantum numbers because they violate the rules that the azimuthal quantum number l must be less than the principal quantum number n, and the magnetic quantum number ml must range from -l to +l.

Step-by-step explanation:

The student's question involves identifying which sets of quantum numbers are not possible. Each quantum number has specific rules:

• The principal quantum number n must be a positive integer.
• The azimuthal quantum number l can be any integer from 0 to n-1.
• The magnetic quantum number ml can be an integer from -l to +l.
• The spin quantum number ms can only be +1/2 or -1/2.

Using these rules, we can determine the following sets as not possible:

• D. n = 1, l = 2, ml = 0, ms = +1/2 (Since l must be less than n, l cannot be 2 when n is 1.)
• E. n = 3, l = 2, ml = 3, ms = +1/2 (Since ml can only range from -l to +l, ml cannot be 3 when l is 2.)
• F. n = 5, l = -4, ml = 3, ms = -1/2 (Since l must be a non-negative integer and less than n, l cannot be -4.)

All other sets of quantum numbers provided are possible because they adhere to the prescribed quantum number rules.