Question

What will be the mass of one atom of nitrogen? (Molar mass of nitrogen is $ 14 $ u)

Answer 1

Hint: We know that the one mole of any substance comprises $ 6.023\times {{10}^{23}} $ particles. We can call the value of $ 6.023\times {{10}^{23}} $ as Avogadro number (or) Avogadro constant and is represented by the symbol $ {{N}_{A}} $ . We can calculate the mass of an atom by the moles of one atom and Avogadro number.

Complete answer:
We know that one mole of atoms contains Avogadro number of particles. If you know the mass of one mole of an atom that is gram atomic mass (GAM), you can solve this problem easily. We must remember that the SI $ \left( mol{{e}^{-1}} \right) $ of Avogadro number is a reciprocal mole. We know that the Avogadro number is dimensionless. We can also relate the molar volume of a substance to the average volume occupied by one of the particles, when the units of volume are in the same quantity using Avogadro constant number. Now let us calculate the mass of one atom of nitrogen. We can calculate the mass of one atom of nitrogen by dividing the mass of one mole of nitrogen to the Avogadro number of atoms.
According to Avogadro’s law, one mole of every substance contains particles and weighs equal to the molar mass of the substance. The mass of one mole of nitrogen atom will be. We know that one mole of a particle will contain the Avogadro number of atoms. Given molar mass of nitrogen $ =14u=14g $
Thus, atoms of nitrogen weigh $ =14\text{ }gram. $
 $ \therefore 1 $ atom of nitrogen will weigh $ =\dfrac{14}{6.023\times {{10}^{23}}}\times 1=2.32\times {{10}^{-}}^{23}g. $

Note:
Remember that the number of constituent particles such as molecules, atoms or ions present in a sample is related with mass of the substance in the sample using the proportionality factor called as Avogadro constant or Avogadro number.