Question

One atomic mass unit is equal to:
(A) \[1.66 \times {10^{ - 27}}gm\]
(B) \[1.66 \times {10^{ - 24}}gm\]
(C) \[1.66 \times {10^{ - 23}}gm\]
(D) \[1.66 \times {10^{ - 25}}gm\]

Answer 1

Hint: Atomic mass unit is equal to the mass of the one of the isotopes of carbon divided by a specific positive integer number. \[6.023 \times {10^{23}}\] is known as the Avogadro’s number and it represents the number of units present in one mole.

Complete answer:
In earlier eras of \[{20^{th}}\] century, mass of one hydrogen atom was taken as standard but then the concept of atomic mass unit came. In modern chemistry the carbon-12 isotope means isotope of carbon atom which has molar atomic mass of 12gm is taken as a standard and its mass is taken as 12amu and masses of all the other atoms are decided relative to that mass. Here amu stands for atomic mass unit.
12gm is the weight of 1 mole of carbon atoms, so weight of one carbon-12 atom can be found by dividing weight of 1 mole of carbon-12 atoms by Avogadro number which is equal to \[6.023 \times {10^{23}}\].
So, weight of one carbon-12 atom=\[\dfrac{{{\text{mass of 1 mole of carbon - 12 atoms}}}}{{{\text{Avogadro number}}}}\]
weight of one carbon-12 atom = \[\dfrac{{12}}{{6.023 \times {{10}^{23}}}}\]
weight of one carbon atom = \[1.9924 \times {10^{ - 23}}gm\]
Now it is said that \[1amu = \dfrac{{{\text{Mass of one carbon - 12 atom}}}}{{12}}\]
1amu = \[\dfrac{{1.9924 \times {{10}^{ - 23}}}}{{12}}\]
1 amu = \[0.16603 \times {10^{ - 23}}\] = \[1.6603 \times {10^{ - 24}}\]gm
So , we can say that option (B) \[1.66 \times {10^{ - 24}}gm\] is correct.
So, the correct answer is “Option B”.

Note: Remember that here, in the process of finding the mass of 1 amu, the unit you use to represent mass of the carbon-12 atom, will be the unit of amu. Do not forget that amu is equal to the one twelfth of the mass of one carbon atom, so remember to divide the mass of carbon atom by 12.