(i) An atomic orbital has n = 3. What are the possible values of l and mₗ? (ii) List the quantum numbers (mₗ and l) of electrons for 3d orbital. (iii) Which of the following orbitals are possible? 1p, 2s, 2p and 3f
For an atomic orbital with n = 3, the possible values of l are 0, 1, and 2. The corresponding possible values of m_l are: for l = 0, m_l = 0; for l = 1, m_l = -1, 0, +1; and for l = 2, m_l = -2, -1, 0, +1, +2.
For a 3d orbital, the quantum numbers are n = 3 and l = 2. The possible values of m_l for electrons in a 3d orbital are -2, -1, 0, +1, and +2.
The possible orbitals are 2s and 2p. The 1p orbital is not possible because for n = 1, l can only be 0. The 3f orbital is not possible because for n = 3, the maximum value of l is 2.
Explanation
The values of the azimuthal quantum number (l) are derived from the principal quantum number (n), ranging from 0 to n-1. The magnetic quantum number (m_l) values are derived from l, ranging from -l to +l. For n=3, l can be 0, 1, or 2, corresponding to 3s, 3p, and 3d subshells. A 3d orbital has l=2, giving five possible m_l values. For an orbital to exist, its l value must be less than its n value, making 1p (n=1, l=1) and 3f (n=3, l=3) impossible, while 2s and 2p are valid.