Which of the following sets of quantum numbers is correct for an electron in 4 forbital?

CONCEPT:

Quantum Numbers

• Each electron in an atom is described by a set of four quantum numbers:
  • Principal quantum number (n) – determines the energy level and size of the orbital.
  • Aziral quantum number (l) – determines the shape of the orbital. It can take integer values from 0 to (n-1).
  • Magnetic quantum number (m) – determines the orientation of the orbital in space. It can take integer values from -l to +l.
  • Spin quantum number (s) – determines the spin of the electron, which can be +1/2 or -1/2.
• The allowed values for quantum numbers must adhere to specific restrictions:
  • The value of l must always be less than n (i.e., l = 0, 1, 2, ..., n-1).
  • The magnetic quantum number m must lie between -l and +l, inclusive (i.e., m = -l, ..., 0, ..., +l).

EXPLANATION:

• Statement 1: "n = 4, l = 3, m = +1, s = +1/2"
  • This set of quantum numbers is correct. For n = 4, the value of l can range from 0 to 3. Since l = 3 is valid, m can take any value from -3 to +3. Therefore, m = +1 is a valid value, and s = +1/2 is also a valid spin quantum number.
• Statement 2: "n = 4, l = 4, m = −4, s = −1/2"
  • This set of quantum numbers is incorrect because the value of l cannot be equal to n. Since n = 4, l can range from 0 to 3. Therefore, l = 4 is not valid, making this set of quantum numbers impossible.
• Statement 3: "n = 4, l = 3, m = +4, s = +1/2"
  • This set is incorrect because for l = 3, m must lie between -3 and +3. m = +4 is not a valid value, making this set impossible.
• Statement 4: "n = 3, l = 2, m = −2, s = +1/2"
  • This set of quantum numbers is correct. For n = 3, the value of l can range from 0 to 2. Since l = 2 is valid, m can take values from -2 to +2, and m = -2 is a valid value. Additionally, s = +1/2 is a valid spin quantum number.

Therefore, the correct set of quantum numbers is: "n = 4, l = 3, m = +1, s = +1/2".