State which of the following sets of quantum numbers would...

State which of the following sets of quantum numbers would be possible and which impossible for an electron in an atom. a. $n=2, l=0, m_{l}=0, m_{s}=+\frac{1}{2}$, b. $n=1, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$ c. $n=0, l=0, m_{l}=0, m_{s}=-\frac{1}{2}$ d. $n=2, l=1, m_{l}=-1, m_{s}=+\frac{1}{2}$ e. $n=2, l=1, m_{l}=-2, m_{s}=+\frac{1}{2}^{2}$

State which of the following sets of quantum numbers would be possible and which impossible for an electron in an atom.
a. $n=2, l=0, m_{l}=0, m_{s}=+\frac{1}{2}$,
b. $n=1, l=1, m_{l}=0, m_{s}=+\frac{1}{2}$
c. $n=0, l=0, m_{l}=0, m_{s}=-\frac{1}{2}$
d. $n=2, l=1, m_{l}=-1, m_{s}=+\frac{1}{2}$
e. $n=2, l=1, m_{l}=-2, m_{s}=+\frac{1}{2}^{2}$

Key Concepts

Principal Quantum Number (n)

This quantum number determines the energy level and size of an atomic orbital. It must be a positive integer (n ? 1), thereby controlling the overall energy and radial extent of the electron's probability distribution within an atom.

Angular Momentum Quantum Number (l)

This number is related to the orbital angular momentum of the electron and defines the shape of the orbital. Its value must be an integer in the range 0 ? l ? n - 1, ensuring that the orbital type (s, p, d, f, etc.) is physically valid within a given energy level.

Magnetic Quantum Number (m_l)

This quantum number specifies the orientation of the orbital in space and takes on integer values ranging from -l to +l. It accounts for the different possible spatial orientations of an orbital, which become relevant in the presence of an external magnetic field.

Spin Quantum Number (m_s)

This number represents the intrinsic spin of the electron and has only two possible values: +1/2 or -1/2. It explains the two possible spin states of an electron, which are crucial for the Pauli exclusion principle.

Quantum Number Restrictions

Any set of quantum numbers for an electron must comply with the rules that n is a positive integer, l can only take values from 0 to n - 1, m_l must lie between -l and +l, and m_s is fixed as either +1/2 or -1/2. These restrictions ensure that only physically allowable electron configurations are considered in quantum mechanics.

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