Question

In an atom having 2K,8L,8M and 2N electrons, the number of electrons with m= 0, s= 24 are
(1) 6
(2) 2
(3) 8
(4) 16.

Answer 1

Before answering this question, we should first know that In an element, the electrons are distributed in their atomic orbitals i.e Electronic configuration. It follows a certain procedure or notation where all-electron-containing atomic subshells (the number that is in the superscript) are put in a pattern and sequence.

Complete answer:
The ground state atom is when the lowering of energy of electrons is not possible by transferring the electrons to the different orbitals. This configuration is the most stable one. The electrons in an atom are arranged in a pattern/sequence in shells.
The shells are represented by integer numbers 1,2,3,4 and so on. They are arranged in increasing order of the energy and are called principal quantum numbers.
n= 1,2,3..
The maximum number of electrons that a shell can hold are:
(K) n = 1 is 2
(L) n = 2 is 8
(M) n = 3 is 18
(N) n = 4 is 32
2K has 1 electron at m= 0 ; s =$+\dfrac{1}{2}$
8L has 2 electrons at m= 0 ; s =$+\dfrac{1}{2}$
(Since s and p, both are present.)
8M has 2 electrons at m= 0 ; s =$+\dfrac{1}{2}$
2N has 1 electron at m= 0 ; s= $+\dfrac{1}{2}$
So, total number of electrons at m = 0 and s=$+\dfrac{1}{2}$is (1+2+2+1) = 6

So, Option (1) 6 is correct.

Note:
The azimuthal quantum number refers to the subshells in a shell that are represented by s,p,d,f...
$\ell$=0 to (n-1), the value of $\ell$ can be equal to or greater than 0 and less than or equal to n-1.
The maximum number of electrons in a subshell is given by 2(2$\ell$+1).
So, the maximum number of electrons in the subshell
($\ell$= 0) s is 2
($\ell$= 1) p is 6
($\ell$= 2) d is 10
($\ell$= 3) f is 14