Vaba tee gaasis

Ülesanne. Gaasimolekulide läbimõõt on_{$0 comma 3 space n m. space$}Milline 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_{$9 comma 3 times 10 to the power of negative 8 end exponent space m.$}