Question

How many electrons in a given atom can have the following quantum number?
n = 3, l = 2 , m = $+ 2$ , s = $+ \dfrac{1}{2}$
a. 1
b. 18
c. 14
d. 7

Answer 1

To completely describe an electron in an atom, four quantum numbers are needed i.e. energy (n), angular momentum (l), magnetic moment (m), and spin (s).

Complete step by step answer:
The Principal Quantum Number (n):-The first quantum number describes the electron shell, or energy level, of an atom. The value of n ranges from 1 to the shell containing the outermost electron of that atom.

The Azimuthal Quantum Number(l) :- The second quantum number, known as the angular or orbital quantum number, describes the subshell and gives the magnitude of the orbital angular momentum through the relation.

The Magnetic Quantum Number (m):-The magnetic quantum number describes the energy levels available within a subshell and yields the projection of the orbital angular momentum along a specified axis. The values of l range from $- 1$ to $+ 1$, with integer steps between them.

The Spin Projection Quantum Number (s):-The fourth quantum number describes the spin (intrinsic angular momentum) of the electron within that orbital and gives the projection of the spin angular momentum (s) along the specified axis. An electron has spin s = $\dfrac{1}{2}$ consequently s will be $\pm$, corresponding with spin and opposite spin.

Hence as we now know that quantum no. are required to describe the position, energy and spin of the electron in the atom. So, if we have all four quantum numbers then it just describes only one electron in the following atom.
So, the correct answer is “Option A”.

Note: The main point to be remembered is that 2 electrons can never have the same set of four quantum numbers. If in case 3 quantum numbers are the same then the fourth one will be definitely different.