The mass of a hydrogen molecule is 3.32 x 10^-27 kg. If 10²³ hydrogen molecules strike, per second, a fixed wall of area 2cm² at an angle of 45° to the normal, and rebound elastically with a speed of 10³ m/s, then the pressure on the wall is nearly:

4.70 x 10² N/m²

2.35 x 10³ N /m²

4.70 x 10³ N/m²

2.35 x 10² N /m²

Solution

2.35 x 10³ N /m²

Change in momentum

$∆ P = \frac{P}{\sqrt{2}} \hat{J} + \frac{P}{\sqrt{2}} \hat{J} + \frac{P}{\sqrt{2}} \hat{i} - \frac{P}{\sqrt{2}} \hat{i} ∆ P = \frac{2 P}{\sqrt{2}} \hat{J} = I_{H} m o l e c u l e \Rightarrow I_{w a l l l} = - \frac{2 P}{\sqrt{2}} \hat{J} P r e s s u r e, P = \frac{F}{A} = \frac{\sqrt{2 P}}{A} n (∵ n = n o . o f p a r t i c l e s) \frac{\sqrt{2} x 3.32 x 10^{- 27} x 10^{3} x 10^{23}}{2 x 10^{- 4}} = 2.35 x 10^{3} N / m^{2}$

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