# What is the de Br

We have a relation to find kinetic energy of a gas molecule at any Temperature which is

Where EK is the kinetic energy of a particle at temperature T and K is boltzmann constant

K = 1.38 × 10-23 JK-1

And we know Kinetic energy of a particle is given by the relation

Where vrms is the root meansquare speed of the particle and m is the mass of the particle

So equating both equations we have

On solving we get the root meansquare speed of the particle as

Where Vrms is the root mean square speed of the particle of mass m at temperature T and K is boltzmann constant

K = 1.38 × 10-23 JK-1

Here the temperature is

T = 300K

We are given the particle is a nitrogen molecule (N2) mass of the Nitrogen atom is

mN = 14.0076 u

so mass of N2 molecule is

m = 2 × 14.0076 u = 28.0152 u

converting it to Kg

we know 1 u = 1.66 × 10-27 Kg

so mass of Nitrogen molecule is

m = 28.0152 × 1.66 × 10-27Kg = 46.50 × 10-27Kg

= 4.650 × 10-26Kg

We know de-Broglie wavelength of a particle is given by relation

where 𝜆 is the de de-Broglie wavelength of a particle having mass m and moving with velocity v , here velocity is the root mean square speed of the particle, h is Planck’s constant

h = 6.63 × 10-34 Js

putting the value root mean square speed

in above equation we get

Solving we get the de Broglie wavelength is

Putting value of m,T,K and h in above equation we get

Or 𝜆 = 0.028 × 10-9m = 0.028 nm

So, the de Broglie wavelength of Nitrogen Molecule is 0.028 nm

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Calculate the de-Physics - Board Papers

(a) Plot a graph Physics - Board Papers

Plot a graph showPhysics - Board Papers

Answer the followNCERT - Physics Part-II

An electron (massPhysics - Exemplar