Question

Express unified atomic mass unit in $kg$.

Answer 1

To solve this question we need to know about the definition of unified atomic mass, with the help of which we can express it in $kg$. The unified atomic mass is expressed as $''u''$ and we can say that it is the inverse of Avogadro’s number. Upon using this information, we can express the unified atomic mass $(u)$ in $kg$.

Complete step-by-step solution:
Unified atomic mass $(u)$ can be defined as a unit of atomic and molecular mass. It can be described as one twelfth of the mass of a carbon-$12$ which is at rest and is present in its ground state. Now, to solve this question, we need to know about the relationship between the unified atomic mass $(u)$ and the SI unit of mass i.e., $kg$ which is given by the Avogadro’s number $({{N}_{A}})$. Let us first look at the definition of Avogadro’s number. Avogadro's number means that there are $6.022\times {{10}^{23}}$ units of a substance in one mole of that substance. The unified atomic mass $(u)$ can be written as:
$1u=\dfrac{1}{{{N}_{A}}}$
On substituting the value of Avogadro’s number in the equation, we get:
$\begin{aligned} & 1u=\dfrac{1}{6.022\times {{10}^{23}}} \\\ & \Rightarrow 1u=1.66\times {{10}^{-24}}\text{ gm} \\\ \end{aligned}$
Now, as required in the question, we need to express the value of $1u$ in kilograms. We know that:
$1\text{ kg}=1000\text{ gm}$
Thus,
$1u=1.66\times {{10}^{-27}}\text{ kg}$
Thus, the value of $1$ unified atomic mass expressed in kilograms will be $1.66\times {{10}^{-27}}\text{ kg}$.

Note: To solve such types of questions, the most important part is to remember the definitions of various terms and then use simple conversion to arrive at the final answer. Here in this question, on knowing the definition of unit atomic mass, we just had to convert grams to kilograms.