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 = ${\left( {\dfrac{1}{{12}}} \right)^{th}}{\text{of mass of 1 C atom}}$…………..(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 = $\dfrac{{12}}{{{N_A}}}$g
Now using eqn. 1 , we get
1 amu = $\left( {\dfrac{1}{{12}}} \right) \times \left( {\dfrac{{12}}{{{N_A}}}} \right)g$
Substituting the value of ${N_A}$, we get
1 amu = $\left( {\dfrac{1}{{12}}} \right) \times \left( {\dfrac{{12}}{{6.022 \times {{10}^{23}}}}} \right)g$
$
   = \left( {\dfrac{1}{{6.022 \times {{10}^{23}}}}} \right)g \\
   = 1.660577 \times {10^{ - 24}}g \\
   = 1.660577 \times {10^{ - 27}}kg \\
$
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.