Question

Dual character of electron was explained by:
A. Bohr
B. Heisenberg
C. De Broglie
D. Pauli

Answer 1

Hint: The energy of the electron is stored at a point, just as if it was a particle. And when the electron propagates through space like a wave, it interacts at a point like a particle. This is known as wave-particle duality.

Complete answer
Let us discuss some important points which conclude that electrons have dual character.
1. In 1924, the French scientist, Louis De Broglie suggested that if light has an electron, it behaves as a material particle and a wave.
2. This gives a new wave mechanical theory of matter. According to this theory, small particles like electrons when in motion possess wave properties.
3. According to De-Broglie, the wavelength associated with a moving electron of mass m, with velocity v is given by $\lambda = \dfrac{h}{{mv}}$, h-Planck’s constant.
4. De Broglie also states that the momentum of an electron is quantized i.e. has fixed values.
This is given by $2\pi r = n\lambda $
5. It follows $E = hv = \dfrac{{hc}}{\lambda } = m{c^2}$.
6. It was also verified experimentally by Davisson and Germer experiment by observing diffraction by electron beam.
In this experiment we accelerated an electron by a potential V, then the kinetic energy of electron is $\dfrac{1}{2}m{v^2} = eV$
$\Rightarrow {m^2}{v^2} = 2eVm$
$\Rightarrow mv = \sqrt {2eVm} = P$
$\Rightarrow \lambda = \dfrac{h}{{mv}} = \dfrac{h}{p} = \sqrt {\dfrac{h}{{2eVm}}} $
6. De-Broglie application is applicable to all material objects but the significance is only in the case of microscopic particles. It has no significance in our daily life.
We have read all the important points concluding electrons have dual character.
It was best explained by De-Broglie.

So our correct option: C. De Broglie

Note:
Suppose if we associate Bohr theory with de-Broglie equation then we can conclude $2\pi r = n\lambda $, Where n is the Bohr orbit and r is radius of Bohr orbit.