Question

The mean distance between the atoms of iron is 3\times {{10}^{-10}}m
and interatomic force constant for iron is 7\,N\,/m
The Young?s modulus of elasticity for iron is [JIPMER 2002]
A) 2.33\times {{10}^{5}}\,N/{{m}^{2}} B) 23.3\times {{10}^{10}}\,N/{{m}^{2}} C) 233\times {{10}^{10}}\,N/{{m}^{2}} D) 2.33\times {{10}^{10}}\,N/{{m}^{2}}

Answer 1

This example is an approximation. We are supposed to find the average distance between the molecules in air, and the first approximation is to assume that air only consists of N2 (I know it is only about 78% N2, but this is only an approximation).

The atomic number of N is 14, which gives the molecular mass

2⋅14⋅u≈46⋅10−27kg

where u is representing the atomic mass unit: u≈1.66⋅10−27kg.

The density of air is given as: ρair≈1.3kg/m3.

The volume occupied by 1 molecule can therefore be written as

Vmolecule=mN2ρair≈35⋅10−27m3.