Question

What do you mean by the dual nature of an electron?

Answer 1

1. Louis de Broglie, a French physicist, proposed in 1924 that if light has an electron, it behaves both as a material particle and as a wave.
2. A new wave mechanical theory of matter was presented. Small particles, such as electrons, have wave qualities when in motion, according to this idea.
3. According to de-Broglie, the wavelength of a particle of mass $m$ traveling at velocity $v$ is given by the ratio $\lambda =\frac{h}{mv}$, where $h$= Planck's constant.
4. According to Planck's equation, this can be calculated as follows: $$\begin{gathered} E=hv=\frac{hc}{\lambda } \\ \Rightarrow v=\frac{c}{\lambda } \end{gathered}$$ (photon energy) and based on Einstein's mass-energy relationship, $E=m{c}^2$, Equating both; $$\begin{gathered} \frac{hc}{\lambda }=m{c}^2 \\ or;\lambda =\frac{h}{mc} \end{gathered}$$ This is same as de Broglie relation.
5. Davisson and Germer experimentally confirmed this by observing diffraction effects with an electron beam. If you accelerate an electron with a voltage of V, the Kinetic energy is $$\begin{gathered} \frac{1}{2}m{v}^2=eV \\ \Rightarrow mv=\sqrt{2eVm}=p \\ \Rightarrow \lambda =\frac{h}{\sqrt{2eVm}} \end{gathered}$$.
6. If Bohr's theory is linked to de-equation, Broglie's the wavelength of an electron in Bohr's orbit can be calculated by relating it to circumference and multiplying by a full number $2\pi r=n\lambda$.
7. As a result, $$\begin{gathered} \lambda =\frac{h}{mv} \\ \Rightarrow mvr=\frac{nh}{2\pi } \end{gathered}$$
8. Although the de-Broglie equation applies to all material things, it is only relevant in the case of microscopic particles. Because we come to encounter macroscopic objects in our daily lives, the de-Broglie connection has no practical application.