Q. 194.6( 13 Votes )

# What is the de Br

Answer :

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

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