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The mass of hydrogen molecule is 3.32xx1...

The mass of hydrogen molecule is `3.32xx10^(-27)` kg. If `10^(23)` hydrogen molecules strick per second at 2 `cm^(2)` area of a rigid wall at an angle of `45^(@)` from the normal and rebound back with a speed of 1000 `ms^(-1)`, then the pressure exerted on the wall is

Text Solution

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As the impact is elastic ` therefore |vec(p)_(1)| = |vec(p)_(2)|`= p= mv = `3.32xx10^(-24) kg m//s`
The change in momentum along the normal `Deltap= |vec(p)_(2) - vec(p)_(1)| = 2p "cos"45^(@) = sqrt(2)p`
If f is the collision frequency then force applied on the wall `F= (Deltap)/(Deltat) = Deltap xx f = sqrt(2)pf`
` therefore Pressure P=F/A = (sqrt(2)pf)/(A) = (sqrt(2) xx 3.32 xx 10^(-24) xx 10^(23))/(2xx10^(-4)) = 2.347xx10^(3)N//m^(2)`
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