Very thin films are usually deposited under vacuum conditions to prevent contami

Question

Very thin films are usually deposited under vacuum conditions to prevent contamination and ensure that atoms can fly directly from the source to the depositing surface without being scattered along the way.

a. To get an idea of how few and far between the air molecules are in a thin-film deposition chamber, determine the mean free path of a generic "air" molecule with an effective diameter of 0.25 nm at a pressure of 1.5 x 10-6 Pa and temperature of 300 K.

b. If the chamber is spherical with a diameter of 10 cm, estimate how many times a given molecule will collide with the chamber before colliding with another air molecule.

c. How many air molecules are in the chamber (treating "air" as an ideal gas)?

Explanation / Answer

a. effective diameter of air molecule, d = 0.25 nm = 0.25*10^-9 m

Pressure P = 1.5*10^-6 Pa

temperature, T = 300 K

now mean free path is given by

l = kB*T/sqroot(2)*pi*d^2*P

here kB = boltzmann constant = 8.31/6.022*10^23 = 1.37994*10^-23

so l = 1.3799*10^-23*300/sqroot(2)*pi*(0.25*10^-9)^2*1.5*10^-6

l = 9939.0615 m

b. chamber is spherical with diameter, D = 0.1 m

number of times the molecule will collide with the chamber before collising with the molecule = n

n = l/D = 99390.6155 times

c. usin ideal gas equation

PV = nRT

1.5*10^-6*4*pi*0.05^3/3 = n*8.31*300

n = 3.15*10^-13 moles

number of molecules of air, N = n*6.022*10^23 = 1.8917*10^11

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