Q. 143.8( 16 Votes )

# The wavelength of

Answer :

Now we know de Broglie wavelength of a Particle is given by relation

𝜆 = h/mv

Where 𝜆 is de Broglie wavelength of the particle having mass m and moving with velocity v

But we know momentum is given by relation

p = mv

So, substituting we get de Broglie wavelength of Particle as

𝜆 = h/p

Or we can say momentum of particle is

p = h/ 𝜆

We know kinetic energy of a particle is given by the relation

Where K is the kinetic energy of a particle of mass m moving with velocity v

Now multiplying L.H.S. and R.H.S. of the equation by m we get

or

But we know momentum is given by relation

P = mv

So substituting we get

or

we get kinetic energy of particle K in terms of momentum P and mass of particle m

so putting P = h/ 𝜆

we get kinetic energy of particle as

Where h is the Planck’s constant, m is mass of particle having de Broglie wavelength 𝜆

(a) Now we are given an electron whose de Broglie Wavelength should be

𝜆 = 589 nm = 589 × 10^{-9} m

We know mass of electron is, m = 9.1 × 10^{-31} Kg

and value of Planck’s constant, h = 6.6 × 10^{-34}Js

putting values in the relation to find the kinetic energy of electron K we get

So kinetic energy of the electron is 6.9 × 10^{-25}J

Converting it to eV

1 eV = 1.6 × 10^{-19}J

i.e.

1J = (1/1.6 × 10^{-19})eV

So we get kinetic energy of electron as

Or we get Kinetic energy of electron as 4.31𝜇eV

(b) Now we are given an neutron whose de Broglie Wavelength should be

𝜆 = 589 nm = 589 × 10^{-9} m

We know mass of electron is

m = 1.66 × 10^{-27} Kg

and value of Planck’s constant

h = 6.6 × 10^{-34}Js

putting values in the relation to find the kinetic energy of neutron K we get

So kinetic energy of the electron is 3.78 × 10^{-28}J

Converting it to eV

We know

1 eV = 1.6 × 10^{-19}J

i.e.

1J = (1/1.6 × 10^{-19})eV

So we get kinetic energy of electron as

Or we get Kinetic energy of electron as 2.36 neV

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