Home
Class 12
PHYSICS
What is the de-Broglie wavelength of a n...

What is the de-Broglie wavelength of a nitrogen molecule in air at 300 K? Assume the molecule is moving with the root-mean-square speed of molecules at this temperature. [Atomic mass of nitrogen=14.0076 u].

Text Solution

Verified by Experts

We know that `1u=1.66xx10^(-27)kg` and nitrogen is diatomic gas.
`therefore` Mass of nitrogen molecule`=2xx14.0076xx1.66xx10^(-27)kg=4.649xx10^(-26)kg`
Temperature of nitrogen molecule `T=300K`
`therefore rms` speed of `N_(2)` molecule `v_(rms)=sqrt((3k_(B)T)/(m))`
`therefore` de-Broglie wavelength `lamda=(h)/(mv_(rms))=(h)/(sqrt(3mk_(B)T))=(6.63xx10^(-34))/(sqrt(3xx4.649xx10^(-26)xx1.38xx10^(-23)xx300))`
`=2.8xx10^(-11) m or 0.028nm`.
Promotional Banner

Topper's Solved these Questions

  • DUAL NATURE OF RADIATION AND MATTER

    U-LIKE SERIES|Exercise ADDITIONAL EXERCISES|15 Videos

  • DUAL NATURE OF RADIATION AND MATTER

    U-LIKE SERIES|Exercise CASE BASED/SOURCE-BASED INTEGRATED QUESTIONS|10 Videos

  • CURRENT ELECTRICITY

    U-LIKE SERIES|Exercise SELF ASSESSMENT TEST (SECTION C )|3 Videos

  • ELECTRIC CHARGES AND FIELDS

    U-LIKE SERIES|Exercise SELF ASSESSMENT TEST (SECTION-B) (VERY SHORT ANSWER QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

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 fo molecules at this temperature. (Atomic mass of nitrogen =14.0076U ) Plank's constant= 6.63xx10^(-34)Js , Boltzmann constant =1.38xx10^(-23)JK^(-1)

The root mean square speed of gas molecules

Calculate the root mean square speed of hydrogen molecule at STP

Calculate the root mean square speed of methane molecules at 27^(@)C .

Calucate the root mean square speed of hydrogen molecules at 373.15 K .

Find the rms speed of hydrogen molecules at room temperature ( = 300 K) .

Assertion : The de - Broglie wavelength of a molecule varies inversely as the square root of temperature. Reason : The root mean square velocity of the molecule depends on the temperature.

If the rms speed of the nitrogen molecules of the gas at room temperature is 500 m/s, then the rms speed of the hydrogen molecules at the same temperature will be –