Question

1. An atomic orbital has n = 3. What are the possible values of l and ml?
2. List the quantum numbers (ml and l) of electrons for 3d orbital.
3. Which of the following orbitals are possible?
   1p, 2s, 2p and 3f

Answer 1

1. Possible values of l and m_l

For a given principal quantum number \( n \), the azimuthal quantum number \( l \) can have values: \( 0, 1, 2, \dots, (n-1) \).

• For \( n = 3 \): \( l = 0, 1, 2 \).
• For each \( l \), magnetic quantum number \( m_l \) can have values from \( -l \) to \( +l \) in steps of 1.

So:

• For \( l = 0 \): \( m_l = 0 \).
• For \( l = 1 \): \( m_l = -1, 0, +1 \).
• For \( l = 2 \): \( m_l = -2, -1, 0, +1, +2 \).

2. Quantum numbers (l and m_l) for 3d orbital

“3d” means \( n = 3 \) and \( l = 2 \) (since d-subshell corresponds to \( l = 2 \)).

For \( l = 2 \), possible \( m_l \) values are:

• \( m_l = -2, -1, 0, +1, +2 \).

Thus, for 3d orbital: \( l = 2 \) and \( m_l = -2, -1, 0, +1, +2 \).

3. Which orbitals are possible? (1p, 2s, 2p, 3f)

Rules:

• For a given \( n \), \( l = 0 \) to \( n-1 \).
• s → \( l = 0 \), p → \( l = 1 \), d → \( l = 2 \), f → \( l = 3 \).
• 1p: \( n = 1 \Rightarrow l \) must be 0 only. But p needs \( l = 1 \). So 1p is not possible.
• 2s: \( n = 2, l = 0 \) is allowed. So 2s is possible.
• 2p: \( n = 2, l = 1 \) is allowed. So 2p is possible.
• 3f: \( n = 3 \Rightarrow l = 0, 1, 2 \) only. f needs \( l = 3 \). So 3f is not possible.

Final Answers

• For \( n = 3 \): \( l = 0, 1, 2 \); corresponding \( m_l \): \( 0; -1, 0, +1; -2, -1, 0, +1, +2 \).
• For 3d orbital: \( l = 2 \), \( m_l = -2, -1, 0, +1, +2 \).
• Possible orbitals among 1p, 2s, 2p, 3f: 2s and 2p only.