Question

Population of a country is approximately 100 million. If one mole of rupees is distributed equally among all the peoples, one person will get rupees approximately.
(A)- ${{10}^{15}}$
(B)- $6.22\times {{10}^{14}}$
(C)- $6.022\times {{10}^{15}}$
(D)- 10 million

Answer 1

Hint: In a mole, the number of units amounts for the Avogadro’s constant, that is equivalent to $6.022\times {{10}^{23}}$ in a particular material. So, through the unitary method, you can obtain it for a particular amount.

Complete step by step answer:
Given one mole of rupees is distributed equally among 100 million people. But as we know, one mole of a substance consists of particles equal to Avogadro’s number $({{N}_{A}})$. Then, one moles of rupees will also have ${{N}_{A}}$number of rupees per mole. That is, $1\,mole\,of\,rupees=6.022\times {{10}^{23}}\,rupees\,$. This is distributed among 100 million people. Then, using unitary method, per person will have rupees equal to $=\dfrac{6.022\times {{10}^{23}}}{100\times {{10}^{6}}}=6.022\times {{10}^{15}}$.

Therefore, one person will get rupees approximately equal to option (C)- $6.022\times {{10}^{15}}$rupees.

Additional information: Through the constant, we can also obtain various other relations like between the atomic mass and the molar mass as $Mass(amu)=\dfrac{Molar\,mass(g)}{{{N}_{A}}}$ . Also, like between the Faraday’s constant and charge as $F={{N}_{A}}e$. The constant is found to be equal to the number of atoms in 12 grams of carbon-12. This value was also chosen so that mass of one mole (in grams) is equal to mass of molecule (in Dalton) of compound.

Note: The Avogadro’s number used gives the number of units in one mole of any substance. The unit can be the elementary entity which denotes its quantity collectively, based on the process and the nature of the substance. Thus, the number relates the macroscopic entity to a microscopic entity. It is an absolute number $=6.022\times {{10}^{23}}$ , that is dimensionless and a universal physical constant.