Vaba tee gaasis

Ülesanne. Gaasimolekulide läbimõõt on 0 comma 3 space n m. spaceMilline on gaasimolekulide vaba tee pikkus normaaltingimustel?


Lahendus. Paneme kirja andmed.

Andmed:
d equals 0 comma 3 space n m equals 3 times 10 to the power of negative 10 end exponent space m
n equals 2 comma 7 times 10 to the power of 25 space m to the power of negative 3 end exponent
minus negative negative negative negative negative negative negative negative negative negative negative
lambda equals ?

Normaaltingimustel on ideaalse gaasi ühes kuupmeetris 2 comma 7 times 10 to the power of 25 gaasimolekuli, mille abil oleme leidnud kontsentratsiooni n. Paneme kirja vaba tee rehkendamise valemi

lambda equals fraction numerator 1 over denominator square root of 2 pi d squared n end fraction.

Arvutame:

lambda equals fraction numerator 1 over denominator square root of 2 times 3 comma 14 times left parenthesis 3 times 10 to the power of negative 10 end exponent space m right parenthesis squared times 2 comma 7 times 10 to the power of 25 space m to the power of negative 3 end exponent end fraction equals 9 comma 3 times 10 to the power of negative 8 end exponent space m.

Saime, et vaba tee pikkus on umbes 300 korda suurem kui molekulide läbimõõt.

VASTUS: vaba tee pikkus on 9 comma 3 times 10 to the power of negative 8 end exponent space m.