Question

Problem 33.26

Part A How many molecules strike a 1.00 cm2 surface during 1 minute if the surface is exposed to N2 at 1 atm and 303 K ? Part B Ultrahigh vacuum studies typically employ pressures on the order of 10−10 Torr. How many collisions will occur at this pressure at 303 K ?

Answer 1

Solution- Rate of collision molecules with surface per m^2 per second:
F=P/(2*PIE*mKT)^1/2
Mass of O2 molecule m=32/6.022*10^23=5.314*10^-26 Kg
Boltzamann constant , K=1.381*10^-23 J/K
Temperature=303 K
Area=1.00cm^^2=1.00*10^-4 m^2
Time= 1 min -60 s
1) p= 101325 Pa
F= 101325/(2*3.14*5.314*10^-26*1.381*10^-23*303)
=2.71*10^27 molecular collisions/m^2.s
Number of molecular collision = rate*time*area
=2.71*10^27*60*1.00*10^-4
=1.63*10^25 molecular collisions
2) P= 10^-10 Torr=1.3332*10^-8 pa
F= 1.3332*10^-8/((2*3.14*5.314*10^-26*1.381*10^-23*303)^0.5)
=3.57*10^14 molecular collisions/m^2.s
Number of molecular collisions= rate*time*area
=3.57*10^14*60*1.00*10^-4
=2.14*10^12 molecular collisions