Home
Class 11
PHYSICS
At What temperature will the rms speed o...

At What temperature will the rms speed of oxygen molecules become just sufficent for escaping from the Earth's atmosphere?
(given:mass of oxygen molecule, `m=2.76xx10^(-26)kg,` Boltzmann'sconstant `K_(B)=1.38xx10^(-23)J K^(-1))`

Text Solution

Verified by Experts

The mean square velocity of gas molecule given by `v_(av)=sqrt((2KT)/(m))`
For the molecule to just escape from the earth `v_(av)=v_(e)`
or `sqrt((2KT)/(m))=v_(e)`
`T=(mv_(e)^(2))/(2k)=(5.34 xxx 10^(-26) xx (11.0 xx 10^(3))^(2))/(2 xx 1.38 xx 10^(-23))`
`=2.34 xx 10^(5)K`
Promotional Banner

Similar Questions

Explore conceptually related problems

At what temperature will the average velocity of oxygen molecules be sufficient to escape from the earth. Given mass of oxygen molecule = 5.34 xx 10^(-26) kg . Boltzmann constant, k = 1.38 xx 10^(-23) J "molecule"^(-1) K^(-1) . Escape velocity of earth = 11.0 km s^(-1) .

At what temperature , will the rms speed of oxygen molecules be sufficient for escaping from the earth ? Take m = 2.76 xx 10^(-26) kg, k = 1.38 xx 10^(-23) J//K and v_(e) = 11.2 km//s .

At what temperature, hydrogen molecules will escape from the earth's surface ? (Take, radius of earth R_(e)=6.4xx10^(6)m , mass of hydrogen molecule m=0.34 xx 10^(-26) kg, Boltzmann constant k=1.38xx10^(-23)JK^(-1) and acceleration due to gravity = 9.8 xx ms^(-2) ) also take rms speed of gas as v_(rms) = sqrt((3kT)/(m)) .

Find the average magnitude of linear momentum of a helium molecule in a sample of helium gas at 0^(@)C. Mass of a helium molecule =6.64xx10^(-27)kg and Blotzmann constant =1.38xx10^(-23) J K^(-1).

A gas molecule at the surface of earth happens to have the rms speed for the gas at 0^(@)C . Suppose it went straight up without colliding with other molecules, how high it would rise? Mass of the molecule is 4.65 xx 10^(-26) kg . Boltzmann's constant = 1.38 xx 10^(-23) JK^(-1) .

What is the de-Broglie wavelength of nitrogen molecule in air at 300K ? Assume that the molecule is moving with the root mean square speed of molecules at this temperature. (Atomic mass of nitrogen =14.0076U ) Plank's constant= 6.63xx10^(-34)Js , Boltzmann constant =1.38xx10^(-23)JK^(-1)

What is the de-Broglie wavelength of nitrogen molecule in air at 300K ? Assume that the molecule is moving with the root mean square speed of molecules at this temperature. (Atomic mass of nitrogen =14.0076U ) Plank's constant= 6.63xx10^(-34)Js , Boltzmann constant =1.38xx10^(-23)JK^(-1)

Calculate the average kinetic energy of hydrogen molecule at 0^(@)C . Given k_(B)=1.38xx10^(-23)JK^(-1) .

The temperature ,a t which the root mean square velcity of hydrogen molecules equals their escape velocity from the earth, is closed to: [Boltzmann Constant k_(B)=1.38xx10^(-23)j//K Avogadro Number N_(A)=6.02xx10^(26)//Kg Radius of Earth : 6.4xx10^(6)m Gravitational acceleration On earth = 10ms^(-2)]

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400K, the de Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64 xx 10^(-26) kg, BoItzman constant : 1.38 xx 10^(-23) j//K , Planck constant : 6.63 xx 10^(-34)J.s )