Question

What is $ 1 $ atomic mass unit equal to?

Answer 1

Hint :Start by using the definitions of one amu, one atomic mass unit is defined as a mass exactly equal to one-twelfth the mass of one $ carbon\text{ }\text{ }12 $ isotope atom. It is denoted by the symbol. Use the concept of Avogadro’s constant. Substitute the values and we have to find out the value in the terms of grams (g) or kilograms (kg).

Complete Step By Step Answer:
Let us first see definitions of one a.m.u: One atomic mass unit is defined as a mass exactly equal to one-twelfth the mass of one $ carbon\text{ }\text{ }12 $ isotope atom. Mathematically, it can be written as
 $ 1amu=\left( \dfrac{1}{12} \right)mass(oneCarbonAtom).........(i) $
We know, mass of one mole of $ C\text{ }=\text{ }12\text{ }g $ and one mole of $ C={{N}_{A}}\text{=6}\text{.022}\times \text{1}{{\text{0}}^{\text{23}}}atoms/molecule $
Thus mass of one atom of carbon is equal to $ \dfrac{12}{{{N}_{A}}}g $
Now we have above equation and equation one, we get;
 $ 1amu=\left( \dfrac{1}{12} \right)\times \left( \dfrac{12}{{{N}_{A}}} \right)g $
Now by substituting the values we get;
 $ 1amu=\left( \dfrac{1}{12} \right)\times \left( \dfrac{12}{6.022\times {{10}^{23}}} \right)g $
 $ \Rightarrow 1amu=\left( \dfrac{1}{6.022\times {{10}^{23}}} \right)g $
 $ \Rightarrow 1amu=\left( 1.66\times {{10}^{-24}} \right)g $
Now by converting from grams to kilograms, we get;
 $ \Rightarrow 1amu=\left( 1.66\times {{10}^{-27}} \right)kg $
Therefore, $ 1 $ atomic mass unit is equal to $ 1.66\times {{10}^{-27}}kg $ .

Note :
Students must know important defined terms and their units used in chemistry , as many times questions can be asked in units which are not in general practice . For e.g. to compute atomic weight of oxygen when one 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.