Question

If one mole of carbon atom weighs $12$ g, what is the mass in grams of $1$ atom of carbon?
A. $1.993\times {{10}^{-23}}g$
B. $1.993\times {{10}^{23}}g$
C. $1.993\times {{10}^{-24}}g$
D. $1.993\times {{10}^{24}}g$

Answer 1

The quantity of matter contained in an atom of an element is expressed as a multiple of $1/{{12}^{th}}$ the mass of the carbon$-12$atom. It is given by the value $1.992646547\times {{10}^{-23}}$ grams. This is the atomic mass of $12$ units.

Complete step by step answer:
We know that the $12$ g of carbon is the gram atomic mass of carbon which means one mole of carbon weighs $12$g. Also, we know that the number of atoms or molecules present in one mole of any substance is equal to Avogadro number of atoms or molecules. Avogadro number (${{N}_{A}}$) is equal to $6.022\times {{10}^{23}}$particles. This Avogadro number is a huge number which is used to count extremely small particles line atoms or molecules.
Since, 1 mole of carbon atoms weighs $12$ g, then $6.022\times {{10}^{23}}$carbon atoms also weighs $12$g. Then, the weight of one atom of carbon will be $\dfrac{12}{6.022\times {{10}^{23}}}$ grams which is equal to$1.993\times {{10}^{-23}}g$.
So, mass in grams of one atom of carbon will be$1.993\times {{10}^{-23}}g$. Therefore, the correct option is A.

Note:
When we are dealing with atomic or molecular levels, even one gram of substance contains a huge number of atoms or molecules. Here, we are using the mole concept in order to simplify the calculations. The mole is basically a unit of particles which consists of a very large number of particles which is $6.022\times {{10}^{23}}$ particles.