Question

Mass of hydrogen molecule is $3.3 \times 10^{-27} kg$ and its r.m.s speed at $STP$ is $2500\, m / s$. Number of hydrogen molecules in $2.2\,c. c$. is ________$\times 10^{19}$

Answer 1

$P =\frac{1}{3} \times \frac{ Mc ^{2}}{ V }$
$\therefore P=\frac{1}{3} \times \frac{m N c^{2}}{V}$
Where, $N =$ number of molecules
$\therefore N =\frac{3 PV }{ mc ^{2}} =\frac{3 \times 10^{5} \times 2.2 \times 10^{-6}}{3.3 \times 10^{-27} \times(2500)^{2}}$
$=\frac{2 \times 10^{-1}}{6.25 \times 10^{6} \times 10^{-27}}$
$=\frac{8}{25} \times 10^{20}$
$\therefore N =3.2 \times 10^{19}$