Which of the following is an allowed set of quantum numbers?

• A. n = 2, l = 2, m_l = −2
• B. n = 3, l = 1, m_l = −2
• C. n = 2, l = 1, m_l = −2
• D. n = 4, l = 2, m_l = −2
• E. n = 1, l = 0, m_l = −1

Answer: (D)

Verified step by step guidance

1. Understand the quantum numbers: n (principal quantum number), l (azimuthal quantum number), and ml (magnetic quantum number).
2. The principal quantum number n can be any positive integer (n = 1, 2, 3, ...). It determines the energy level of the electron.
3. The azimuthal quantum number l can be any integer from 0 to n-1. It determines the shape of the orbital.
4. The magnetic quantum number ml can be any integer from -l to +l, including zero. It determines the orientation of the orbital in space.
5. Evaluate each set of quantum numbers: Check if l is within the range 0 to n-1 and if ml is within the range -l to +l for each set.