Final answer:
In quantum mechanics, there are certain restrictions on the values of the quantum numbers that describe the properties of an electron. This answer explains the allowed values for the different quantum numbers and provides examples of allowed and not allowed sets of quantum numbers.
Step-by-step explanation:
In quantum mechanics, there are certain restrictions on the values of the quantum numbers that describe the properties of an electron. The set of quantum numbers {n, l, ms} are allowed, where n represents the principal quantum number, l represents the orbital angular momentum quantum number, and ms represents the spin quantum number.
However, there are certain rules that must be followed:
- The principal quantum number (n) must be a positive integer.
- The orbital angular momentum quantum number (l) must be a non-negative integer and must be less than or equal to n-1.
- The magnetic quantum number (ml) must be an integer between -l and +l, inclusive.
- The spin quantum number (ms) must be either +1/2 or -1/2.
Using these rules, we can determine which sets of quantum numbers are not allowed.
a. {4, 2, -2, 1} - This set of quantum numbers is allowed because it follows all the mentioned restrictions.
b. {3, 1, 0, -1/2} - This set of quantum numbers is not allowed because the orbital angular momentum quantum number (l) must be less than the principal quantum number (n), but in this case, l=1, which is not less than n=3.
The complete question is: Which of the following combinations of quantum numbers is not allowed?
a) n = 1, l = 1, ml = 0, ms = 1/2
b) n = 3, l = 0, ml = 0, ms = -1/2
c) n = 2, l = 1, ml = -1, ms = 1/2
d) n = 4, l = 3, ml = -2, ms = -1/2
e) n = 4, l = 2, ml = 0, ms = 1/2