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 E_{K} 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 v_{rms} 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 V_{rms} 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 (N_{2}) mass of the Nitrogen atom is

m_{N} = 14.0076 u

so mass of N_{2} 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^{-27}Kg = 46.50 × 10^{-27}Kg

= 4.650 × 10^{-26}Kg

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^{-9}m = 0.028 nm

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

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