Question

The total number of protons, electrons and neutrons in $12\,g$ of $_6^{12}C$ is equal to:
A. $1.084 \times {10^{25}}$
B. $6.022 \times {10^{23}}$
C. $6.022 \times {10^{22}}$
D. $36.13 \times {10^{23}}$

Answer 1

Hint: The relative atomic mass unit is based on relative scale and mass of $^{12}C$ (carbon twelve) and it is defined as $12\,amu$. The mole is a measurement for the amount of substance present in $1\,mole$ of any substance contains a specific number of particles.

Complete step by step solution:
Mole is a unit of measurement for the amount of substance in an international system of units. A mole of substance or a mole of particles is defined as exactly $6.022 \times {10^{23}}$ particles, which can be atoms, molecules, ions or electrons, protons, neutrons.
The number $6.022 \times {10^{23}}$ is also known as Avogadro number. It denotes that the mass of one mole of a chemical compound in grams is numerically equal to the average mass of one molecule of the compound in Daltons. For example water. One mole of water contains $6.022 \times {10^{23}}$ molecules whose mass is $18g$, this also means one molecule of water is about 18 Dalton.
Now for $12\,g$ of (carbon twelve) $_6^{12}C$. Its atomic mass is $12\,amu$, that means it contains $6.022 \times {10^{23}}$ atoms of $_6^{12}C$.
So the total number of atoms of $_6^{12}C$ .= $6.022 \times {10^{23}}$.
We know that, Atomic number = Number of protons = Number of electrons
Now for $_6^{12}C$, Number of protons = Number of electrons = 6
$\Rightarrow$ Number of neutrons = Atomic mass – Number of protons
Number of neutrons = 12 – 6 = 6
So, Total number of electrons = $6 \times 6.022 \times {10^{23}}$ $ = 36.132 \times {10^{23}}$ in $12g$ of $_6^{12}C$
Similarly, Total number of protons = $6 \times 6.022 \times {10^{23}}$$12g$ $ = 36.132 \times {10^{23}}$ in $12g$ of $_6^{12}C$
Total number of neutrons = $6 \times 6.022 \times {10^{23}}$$12g$ $ = 36.132 \times {10^{23}}$ in $12g$ of $_6^{12}C$.
In the question, it is asked the total number of electrons, proton and neutron so we add all the three.
We get total number of electrons, protons, neutrons $ = (36.132 + 36.132 + 36.132) \times {10^{23}}$
 $
   = 108.39 \times {10^{23}} \\
   = 1.08 \times {10^{25}}
 $

Therefore the correct option will be A.

Note:
When we write a chemical equation, the quantities are assumed to be in moles, that means if 1 mole of first reactant will react with one mole of second, that clearly means $6.022 \times {10^{23}}$ particles of first reactant will react with $6.022 \times {10^{23}}$ particles of second reactant.