Question

An an atom which has $2$K, $8$L, $16$M and$2$N electrons in the group the total no, of electrons having ${\text{l}}\,{\text{ = }}\,{\text{1}}$ are:
A.$20$
B.$8$
C.$12$
D.$12$

Answer 1

Hint: To answer this question we should know what K, L, M, and N and ${\text{l}}\,{\text{ = }}\,{\text{1}}$represents. So, we should have knowledge of quantum numbers. First we will write the electronic configuration from the given information. Then we will count the electrons having ${\text{l}}\,{\text{ = }}\,{\text{1}}$.


Complete solution:
Electronic configuration of an atom has four quantum numbers.
Principle quantum number: it tells the energy level or shell.
Its value ranges from $1 - \infty $.
The name of energy level is given by alphabets which are shown as follows:

Energy level	Name of the level
1	K
2	L
3	M
4	N

Azimuthal quantum number: it tells the orbital.
Its value ranges from $0 - ({\text{n}} - 1)$.
Magnetic quantum number: It tells the orbital of the subshell.
Its value ranges from $( - {\text{l)}}\, - ({\text{ + l}})$.
It is determined by ${\text{2l}}\,{\text{ + }}\,{\text{1}}$.
Spin quantum number: It tells the spin of an electron.
Its value is $ - 1/2$ or $ + 1/2$.
Now, we will write the electronic configuration from the given information as follows:
$2$K, means K-shell has two electrons in s-orbital, $8$L means L-shell has eight electrons, two in s and six in p-orbital, $16$M means M-shell has sixteen electrons, two in s, six in p and eight in d-orbital, and$2$N means N-shell has two electrons is s-orbital.
Now, we have to find the electrons having ${\text{l}}\,{\text{ = }}\,{\text{1}}$, ${\text{l}}\,{\text{ = }}\,{\text{1}}$ means p-orbital. From the above electronic configuration we can tell that six electrons are present in $2$p-orbital of L-shell and six electrons are present in $3$p-orbital of M-shell.
So, a total of twelve electrons are present in ${\text{l}}\,{\text{ = }}\,{\text{1}}$.
So, the total no, of electrons having ${\text{l}}\,{\text{ = }}\,{\text{1}}$ are $12$.

Therefore, option (C) and (D) $12$ both are correct.


Note: The number of energy levels represents the number of orbital present in it such as energy level one that is K has one orbital only that is s-orbital. Similarly, energy level two that is L-shell has two orbitals s and p. the number of maximum electrons in a shell is determined by ${\text{2}}{{\text{n}}^{\text{2}}}$ . Where n is the number of energy levels. We can also determine the number of electrons having ${\text{l}}\,{\text{ = }}\,0$ and ${\text{l}}\,{\text{ = }}\,2$.