Question

Sum of number of protons, electrons, and neutron in 12g of ${^{12}_6}C$ is:
A. $1.8$
B. $12.044\, \times \,{10^{23}}$
C. $1.084\, \times \,{10^{25}}$
D. $10.84\, \times \,{10^{24}}$

Answer 1

Hint:In order to answer this question you must recall the mole concept in which you have done conversions regarding the number of moles, number of atoms, number of electrons, protons, and neutrons in a sample of given weight. Firstly, find the number of moles of the given sample and use the Avogadro number and the unitary method to find the number of protons, electrons, and neutrons and then sum these three values and you will get your answers.

Complete answer:
Step 1: In this step we will find the number of moles of the given sample:
Number of moles of a sample = $\dfrac{{Given\,Weight}}{{Molecular\,Weight}}$
 Number of moles in 12g of carbon = $\dfrac{{12}}{{12}}\, = \,1\,mole$
Step 2: In this step we will find the number of atoms in 1 mole of carbon:
Number of atoms in 1 mole of carbon = $1 \times {N_A}\, = \,$ $6.023 \times {10^{23}}$
Since we know that, 1 mole of carbon contains 6 electrons, 6 protons and 6 neutrons.
Step 3: In this step we will find the number of electrons in 1 mole of carbon:
Number of electrons in 1 mole of carbon = $6 \times 6.023 \times {10^{23}}\,$
Step 4: Similarly, in this step we will find the number of protons in 1 mole of carbon:
Number of protons in 1 mole of carbon = $6 \times 6.023 \times {10^{23}}\,$
Step 5: Similarly, in this step we will find the number of neutrons in 1 mole of carbon:
Number of neutrons in 1 mole of carbon = $6 \times 6.023 \times {10^{23}}\,$
Step 6: Now, we will sum all the three values:
Sum of electrons, protons and neutrons = $6 \times 6.023 \times {10^{23}}\, + \,6 \times 6.023 \times {10^{23}}\, + \,6 \times 6.023 \times {10^{23}}\,$
= $3 \times \left( {6 \times 6.023 \times {{10}^{23}}\,} \right) = \,10.84 \times {10^{24}}\, = \,1.084 \times {10^{25}}$

Clearly, the correct answers are options C and D. (both options contain the same value so either of them will also be the correct answer if the question is given in single correct format.

Note:
The number $6 \times 6.023 \times {10^{23}}\,$ is popularly known as the Avogadro constant and is often denoted by the symbol $'{N_A}'$. The elementary entities that can be represented in moles can be atoms, molecules, monoatomic/polyatomic ions, and other particles (such as electrons).