Question

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

Answer 1

Answer: 3.2

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