Multiple Choice
Which statement best describes the relationship between the principal quantum number n, the energy of an orbital, and its average radius in a hydrogen atom?
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9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which property of an atomic orbital is determined by the principal quantum number (n)?
A
The spin direction of the electron
B
The orientation of the orbital in space
C
The energy level and relative size of the orbital
D
The shape of the orbital
Verified step by step guidance1
Understand that the principal quantum number, denoted as \(n\), is one of the four quantum numbers used to describe the properties of an electron in an atom.
Recall that \(n\) primarily determines the energy level of the electron within the atom, which corresponds to the shell or main energy level the electron occupies.
Recognize that as \(n\) increases, the orbital's average distance from the nucleus increases, which means the relative size of the orbital also increases.
Note that other properties such as the shape of the orbital are determined by the azimuthal quantum number (\(l\)), the orientation in space by the magnetic quantum number (\(m_l\)), and the spin direction by the spin quantum number (\(m_s\)).
Therefore, the principal quantum number \(n\) determines the energy level and relative size of the atomic orbital.
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