state and explain de broglie s principal for duatism of electron
Answers
Answer:
de Broglie equation states that a matter can act as waves much like light and radiation, which also behave as waves and particles. The equation further explains that a beam of electrons can also be diffracted just like a beam of light. In essence, the de Broglie equation helps us understand the idea of matter having a wavelength.
Therefore, if we look at every moving particle whether it is microscopic or macroscopic it will have a wavelength.
In cases of macroscopic objects, the wave nature of matter can be detected or it is visible.
Very low mass particles moving at speed less than that of light behave like a particle and wave. De Broglie derived an expression relating the mass of such smaller particles and its wavelength.
Plank’s quantum theory relates the energy of an electromagnetic wave to its wavelength or frequency.
E = hν =\frac{hc}{\lambda }=
λ
hc
…….(1)
Einstein related the energy of particle matter to its mass and velocity, as E = mc2……..(2)
As the smaller particle exhibits dual nature, and energy being the same, de Broglie equated both these relations for the particle moving with velocity ‘v’ as,
E = =\frac{hc}{\lambda }=m{{v}^{2}}:=
λ
hc
=mv
2
: Then, \frac{h}{\lambda }=mv
λ
h
=mv or \lambda =\frac{h}{mv}=\frac{h}{\text{momentum}}:λ=
mv
h
=
momentum
h
: where ‘h’ is the Plank’s constant.
This equation relating the momentum of a particle with its wavelength is de Broglie equation and the wavelength calculated using this relation is de Broglie wavelength.
Answer:
State and explain de broglie s principal for duatism of electron