Question

One atomic mass unit (a.m.u ) is equal to?
a.) $2.67377\times {10}^{-27}$kg
b.) $1.67377\times {10}^{-22}$kg
c.) $0.67377\times {10}^{-27}$kg
d.) $1.66057\times {10}^{-27}$kg

Answer 1

Hint: Start by using the definition of 1 amu , One atomic mass unit is defined as a mass exactly equal to one-twelfth the mass of one carbon – 12 isotope atom. It is denoted by the symbol $u$. Use the concept of Avogadro’s constant . Substitute the values and find the value in the terms of grams(g) or kilograms(kg).

Complete step by step answer:
Let us first see the definition of 1 a.m.u :-
One atomic mass unit is defined as a mass exactly equal to one-twelfth the mass of one carbon – 12 isotope atom.
Mathematically , it can be written as
1 amu = ${\left({\displaystyle \frac{1}{12}}\right)}^{th}\text{of mass of 1 C atom}$…………..(eqn. 1 )
We know , mass of 1 mole of C = 12 g
And 1 mole of C = $=N_A=6.022\times {10}^{23}$atoms/molecule
Therefore , mass of 1 atom of C = ${\displaystyle \frac{12}{N_A}}$g
Now using eqn. 1 , we get
1 amu = $\left({\displaystyle \frac{1}{12}}\right)\times \left({\displaystyle \frac{12}{N_A}}\right)g$
Substituting the value of $N_A$, we get
1 amu = $\left({\displaystyle \frac{1}{12}}\right)\times \left({\displaystyle \frac{12}{6.022\times {10}^{23}}}\right)g$
$$\begin{gathered} =\left({\displaystyle \frac{1}{6.022\times {10}^{23}}}\right)g \\ =1.660577\times {10}^{-24}g \\ =1.660577\times {10}^{-27}kg \end{gathered}$$
Therefore , 1 amu $=1.660577\times {10}^{-27}kg$
So, the correct answer is “Option D”.

Note: Students must know important definitions , terms and their units used in chemistry , as many times questions can be asked in units which are not in general practise . For e.g. To compute atomic weight of oxygen when 1 amu is defined keeping Nitrogen as reference. Then in that case use the same procedure as we followed but use Nitrogen as reference with given data.