Q. An electron tube was sealed off during manufacture at a pressure of $1.2 \times 10^{- 7}mm$ of mercury at $27℃$. Its volume is $100\ cm^{3}.$ The number of molecules that remain in the tube is
A) $2 \times 10^{16}$
B) $3 \times 10^{15}$
C) $3.86 \times 10^{11}$
D) $5 \times 10^{11}$
Explanation
(c) Gas equation for $N$ molecules $PV = NkT$
$\Rightarrow N = \frac{PV}{kT} = \frac{1.2 \times 10^{- 10} \times 13.6 \times 10^{3} \times 10 \times 10^{- 4}}{1.38 \times 10^{- 23} \times 300}$
$= 3.86 \times 10^{11}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.