Q. 124.3( 14 Votes )
Calculate the
Answer :
(a) When an charged particle having charge q is accelerated by a potential difference V volts it gain kinetic energy given by
K = Vq, which imparts it with velocity
We know kinetic energy of a Particle with mass m kg and velocity v is given by
Equating both equations
We get velocity of the particle as
But we know momentum is given by relation
P = mv
Where P is the momentum of particle having mass m and moving with velocity v
So we get
Here Potential difference
V = 56 volts
q = 1.6 ร 10-19 C
m = 9.1 ร 10-31Kg
so momentum of the electron,
So momentum of electron is 4.04 ร 10-24 Kgms-1
(b) Now we know de Broglie wavelength of a Particle is given by relation
๐ = h/mv
Where ๐ 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
Where P is the momentum of particle having mass m and moving with velocity v
So substituting we get de Broglie wavelength of Particle as
๐ = h/P
h = 6.6 ร 10-34Js
p = 4.04 ร 10-24 Kgms-1
So putting the values in equation we get
So the de Broglie wavelength of electron is 0.164 nm
Note: we could have also used the direct relation when an electron is accelerated through a potential difference of V volts its de Broglie wavelength is given by
1Ao = 10-10m
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