Question

Find the potential energy of a system of four particles placed at the vertices square of side 'a' .Also obtain the potential at the center of the square
(i) The size of hydrogen atom is about 0.4 A. Calculate the total volume $\left(in{m}^3\right)$ of a mole of hydrogen atom?Give $1A={10}^{-10}m$

Answer 1

(a) Let four objects are at A,B,C and D of a square of side l

Total potential energy of the system is

$-[\frac{G{M}_a{M}_b}{1}+\frac{G{M}_a{M}_c}{1/\sqrt{2}}+\frac{G{M}_a{M}_d}{1}]$

$\because M_a=M_b=M_c=M$

$so,$

$-[\frac{G{M}^2}{1}+\frac{G{M}^2}{1/\sqrt{2}}+\frac{G{M}^2}{1}]$

$\left[\frac{G{M}^2}{1}\right](2+\sqrt{2})$

This is the potential energy of the system of particles.

(2) It is given that,

Radius $r=0.4\times {10}^{-10}m$

Volume is

$V=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\times 3.14\times {(0.4\times {10}^{-10})}^3$

$V=0.26\times {10}^{-30}{m}^3$

So, volume of 1 mole of Hydrogen

$V=6.023\times {10}^{23}\times 0.26\times {10}^{-30}$

$V=1.56\times {10}^{-7}{m}^3$