Multiple Choice
For a 3s^2 electron in phosphorus (atomic number 15, electron configuration: 1s^2 2s^2 2p^6 3s^2 3p^3), what is the value of the third quantum number (magnetic quantum number, m_l) for this electron?
9. Quantum Mechanics
Quantum Numbers: Principal Quantum Number
Multiple Choice
Which statement correctly describes the principal quantum number n for an electron in the state n=4, l=3, m=2, s=1/2?
A
It indicates the orientation of the orbital in space.
B
It describes the spin direction of the electron.
C
It determines the energy level and relative size of the orbital.
D
It specifies the shape of the orbital.
Verified step by step guidance1
Understand that the principal quantum number \(n\) is one of four quantum numbers that describe the state of an electron in an atom.
Recall that the principal quantum number \(n\) primarily determines the energy level of the electron and the relative size of the orbital where the electron is likely to be found.
Recognize that the other quantum numbers have different roles: the azimuthal quantum number \(l\) specifies the shape of the orbital, the magnetic quantum number \(m\) indicates the orientation of the orbital in space, and the spin quantum number \(s\) describes the spin direction of the electron.
Given the electron state \(n=4\), \(l=3\), \(m=2\), \(s=\frac{1}{2}\), identify that \(n=4\) corresponds to the fourth energy level and a larger orbital size compared to lower \(n\) values.
Therefore, the statement 'It determines the energy level and relative size of the orbital' correctly describes the principal quantum number \(n\).
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