Which of the following orbitals possesses the most orbital shapes?

• A. 2p
• B. 7s
• C. 4d
• D. 5p
• E. 5f

Answer: (E)

Verified step by step guidance

1. Understand that the number of orbital shapes is determined by the azimuthal quantum number (l), which is related to the type of orbital: s, p, d, f, etc.
2. Recall that the azimuthal quantum number (l) for s orbitals is 0, for p orbitals is 1, for d orbitals is 2, and for f orbitals is 3.
3. Recognize that the number of possible shapes for a given type of orbital is determined by the number of magnetic quantum numbers (m_l), which range from -l to +l.
4. Calculate the number of shapes for each type of orbital: s has 1 shape (m_l = 0), p has 3 shapes (m_l = -1, 0, +1), d has 5 shapes (m_l = -2, -1, 0, +1, +2), and f has 7 shapes (m_l = -3, -2, -1, 0, +1, +2, +3).
5. Compare the number of shapes for each orbital type given in the problem: 2p (3 shapes), 7s (1 shape), 4d (5 shapes), 5p (3 shapes), and 5f (7 shapes). The 5f orbital has the most shapes.