Question

In the ground state of \[{\text{Kr}}\] atom, how many electrons have the quantum number \[{{\text{m}}_l} = - 2\]?

Answer 1

Hint: We know that the lowest energy state for an electron is its ground state, which is the energy level it normally occupies. Each electron has maximum energy that it can have while still being a component of its atom. The electron is no longer bound to the nucleus of the atom once it reaches that energy level, and it is said to be ionized. An electron is in an excited state when it temporarily occupies an energy state higher than its ground state.

Complete answer:
The orientation of the orbital in which an electron is placed in an atom is described by the magnetic quantum number, \[{{\text{m}}_{\text{l}}}\]. The magnetic quantum number's values are determined by the angular momentum quantum number, l, which indicates the energy subshell in which an electron is located.
To have a value of \[{{\text{m}}_l} = - 2\], l must have a value as follows
\[{\text{l}} \geqslant {\text{2}}\]
The angular momentum l can take the following values,
l=0→ describes the s subshell
l=1→ describes the p subshell
l=2→ describes the d subshell and so on.
We know that krypton is located in the period \[4\], group \[18\] of the periodic table.
\[{\text{K = 1}}{{\text{s}}^2}2{s^2}2{p^6}3{s^2}3{p^6}3{d^{10}}4{s^2}4{p^6}\]
For d- subshell,
\[{m_l} = \{ - 2, - 1,0,1,2\} \]
In a neutral atom of krypton, there are \[10\] electrons in the \[3d\]subshell. It is the only d subshell that contains electrons in this atom. Each of the five \[3d\]orbitals will contain \[2\] electrons which are of opposite spins.
So, two electrons will have \[{{\text{m}}_l} = - 2\].
Hence, the answer is \[2\] electrons.

Note:
It can be noted that in this case, we are particularly looking for the number of d subshells present in the krypton atom when the atom is in a neutral state as well as in its ground state. We are then looking for the number of electrons located in one of the five d orbitals which is present for every d subshell having electrons. As we know that the d subshell has five d orbitals. In this way, we were able to find out the number of electrons having \[{{\text{m}}_l} = - 2\].