Question

One atomic mass unit is equivalent to
A.\[1.67 \times {10^{ - 27}}g\]
B.\[1.66 \times {10^{ - 27}}kg\]
C.\[1.67 \times {10^{ - 27}}mg\]
D.\[1.6 \times {10^{ - 24}}g\]

Answer 1

Hint:For this we must know the definition of atomic mass unit. We calculate the mass of atoms in an atomic mass unit. For example \[C\] has an atomic mass of 12 amu.

Complete step by step solution:
Atoms are very small; hence it is very difficult to calculate its mass. That is why we always take a reference to calculate the mass of an atom. Mass of an atom is calculated by addition of mass of neutrons and electrons. Neutrons and protons are together called nucleons. We know the mass of both neutrons and protons is the same, that is \[1.67 \times {10^{ - 27}}kg\]. So,
  {\text{mass of atom = mass of nucleons}} \\
  {\text{ = number of nucleons}} \times 1.67 \times {10^{ - 27}}kg \\
We know mass number is the sum of the number of neutrons and protons and is represented as A.
\[{\text{mass of atom = A}} \times {\text{a}}{\text{.m}}{\text{.u}}\]
Comparing both the equations we will get \[{\text{1 a}}{\text{.m}}{\text{.u}} = 1.67 \times {10^{ - 27}}{\text{kg}}\]
Initially for the calculation of atomic mass unit hydrogen was taken as a reference, but it did not give any significant results because it was not suitable for calculation of mass for most of the elements. so we switched to carbon.
According to this 1 a.m.u is one twelfth of the mass of the carbon 12 isotope which is basically\[1.66 \times {10^{ - 27}}kg\]. The actual formula of atomic mass unit is:
\[{\text{relative mass of atom}} = \dfrac{{{\text{mass of atom}}}}{{{\text{mass of C}} - 12{\text{ isotop}} \times \dfrac{1}{{12}}}}\]
Hence the correct option is B.

Note:as we have seen that the atomic mass unit is a very small unit so instead of that we use moles as a unit. It is a unit to determine the amount of substance. \[1{\text{ mole = 6}}{\text{.022 }} \times {\text{ 1}}{{\text{0}}^{23}}{\text{ molecules}}\]. Whenever we say the mass or mass number of hydrogen is 1 that means its mass is one atomic mass unit or amu.