Multiple Choice
Which set of quantum numbers is not possible for an electron in an atom?
9. Quantum Mechanics
Quantum Numbers: Angular Momentum Quantum Number
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Which of the following orbitals possesses the most orbital shapes?
A
2p
B
7s
C
4d
D
5p
E
5f
Verified step by step guidance1
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.
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.
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.
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).
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.
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