Question

The mass of a hydrogen molecule is $3.32\times {10}^{-27}$ kg. If ${10}^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2c{m}^2$ at an angle of ${45}^o$ to the normal, and rebound elastically with a speed of ${10}^{3}m/s$, then the pressure on the wall is nearly.

• A. $2.35\times {10}^2$ $N/m^2$
• B. $4.70\times {10}^2$ $N/m^2$
• C. $2.35\times {10}^3$ $N/m^2$
• D. $4.70\times {10}^3$ $N/m^2$

Answer 1

The correct option is C $2.35\times {10}^3$ $N/m^2$

Given : $u={10}^{3}m/s$ $m=3.32\times {10}^{-27}kg$ $n={10}^{23}$ $H_2$ molecules per sec.
Change in momentum along y-axis of one $H_2$ molecule $\Delta P=mu\cos {45}^o-(-mu\cos {45}^o)$
$⟹\Delta P=2mu\cos {45}^o$
Total change in momentum along y-axis of all $H_2$ molecule in one second $\Delta P_T=2nmu\cos {45}^o$
Area of the wall $A=2c{m}^2=2\times {10}^{-4}{m}^2$
Net pressure $P=\frac{\Delta P_T}{A}=\frac{2\times {10}^{23}\times 3.32\times {10}^{-27}\times {10}^3\times 0.707}{2\times {10}^{-4}}=2.35\times {10}^{3}N/m^2$