Question

In \[Ca\]atom how many electrons contain \[m=0\]
A. 12
B. 8
C. 10
D. 18

Answer 1

Hint: Each shell can contain just a fixed number of electrons: The principal shell can hold up to two electrons, the subsequent shell can hold up to eight \[\left( 2+6 \right)\] electrons, the third shell can hold up to \[18\left( 2+6+10 \right)\], etc. The overall equation is that the nth shell can on a fundamental level hold up to \[2\left( {{n}^{2}} \right)\]electrons.

Complete step by step answer:
A quantum number is a worth that is utilized while portraying the energy levels accessible to particles and atoms. An electron in an iota or particle has four quantum numbers to depict its state and yield answers for the Schrödinger wave condition for the hydrogen molecule.
Calcium; \[Z=20\]
Electronic configuration: \[1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{2}}\]
\[1s,2s,2p,3s,3p\] and \[4s\] are the subshells involved.
Each subshell has one orbital for which magnetic quantum number is zero. Due to magnetic quantum values lies between \[-1\] to \[+1\] where l is the Azimuthal quantum number.
For s-subshell, l=0 ∴ values of magnetic quantum number is 0.
For p-orbital, l=1 ∴ values of magnetic quantum numbers are -1, 0, 1.
In calcium, 6 orbitals for which magnetic quantum number is zero. So \[12\left( 6*2 \right)\]electrons whose magnetic quantum number is zero.
Total numbers of electrons present,
\[1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}3{{d}^{0}}4{{s}^{2}}\]
\[2+2+2+2+2+2=12e^-\]

Hence, the correct option is A. 12

Note:
The arrangement of numbers used to portray the position and energy of the electron in an iota are called quantum numbers. There are four quantum numbers, specifically, principal, azimuthal, magnetic and spin quantum numbers. The estimations of the rationed amounts of a quantum framework are given by quantum numbers.