Question

The mass of one atom of $Carbon-12$is:
A. $1g$
B. $12g$
C. $12\times 6.02\times {{10}^{23}}g$
D. $\dfrac{12}{6.02\times {{10}^{23}}}g$

Answer 1

Hint: One mole of any element contains $6.02\times {{10}^{23}}$atoms. And we know that the mass of one mole of an element is equal to its molar mass. So, the mass of $6.02\times {{10}^{23}}$atoms will be equal to its molar mass or atomic weight. You got the mass of $6.02\times {{10}^{23}}$atoms. So, then find out the mass of one atom of any element using the given information.


Complete step by step solution:
As per the given question, the element given is $Carbon-12$ atom.
We know that one mole of any element will be equal to its molar mass or atomic weight in grams.
And,
Here, the atomic weight of carbon is $12g$.
So, one mole of carbon atom will weigh $12g$.
We also know that; a mole is defined as exactly equal to $6.02\times {{10}^{23}}$atoms.
Therefore, we can write the mass of $Carbon-12$ as,
$6.02\times {{10}^{23}}atoms=12g$.
Using the unitary method, we can now find out the mass of one atom of carbon in grams. So, we can write as below:
If, mass of $6.02\times {{10}^{23}}atoms=12g$,then
Mass of one atom will be?
So, now mass of one atom of carbon will be $=\dfrac{12}{6.02\times {{10}^{23}}}g$, which will be equal to $1.993\times {{10}^{23}}g$.
Thus, the mass of one atom of carbon in grams will be $\dfrac{12}{6.02\times {{10}^{23}}}g$.
Likewise, if we have to find out the mass of two atoms or n number of atoms, the same way we can proceed using the unitary method to find the mass in grams of that atom.

Hence, the correct option is D.


Note: While solving the question, the first thing to remember is about mole. A mole equals to exactly $6.02\times {{10}^{23}}$ of some chemical units, whether it be atoms, molecules, ions, or others. Also, a mole refers to the molar mass of that element. So, we have got the mass of one mole of atoms, and now we can easily find the mass of one atom.