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The wave nature of electron was verified by:
A. De broglie
B. Davisson Germer
C. G.P. Thomson
D. Rutherford

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Answer
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Hint: De Broglie gave a hypothesis of the dual nature of particles and waves. This hypothesis is confirmed by the Davisson Germer experiment. G.P. Thomson did a cathode ray tube experiment and found the negatively charged subatomic particle. Rutherford did the gold foil experiment.

Complete step by step answer:
The waves have a dual nature. De-Broglie said that the matter also has dual nature. The matter that has linear momentum also has a wave associated with it. The De-Broglie equation gives the relation between wave nature and particle nature. So, the wave nature of the electron was verified by De-Broglie so option (A) is correct.
Davisson Germer fires an electron beam on the metal surface. In this experiment, they got diffraction patterns of the electrons beam which is the property of the wave. By this experiment, they confirmed that the matter particle such as electrons also has wave-like nature. So, the wave nature of the electron was verified by Davisson Germer, so option (B) is correct.
G.P. Thomson passed electrons beam through the celluloid and got a diffraction pattern and told that electrons are particles. . So, the wave nature of the electron was not verified by G.P. Thomson so, option (C) is incorrect.
Rutherford did a gold foil experiment in which he bombarded alpha particles on the gold foil. The alpha particle collides with the gold atom and gets scattered. Based on observation Rutherford told that an atom has a dense positively charged centre that is the nucleus. So, the wave nature of the electron was not verified by Davisson Germer, so option (D) is incorrect.

Therefore, option (A) de Broglie and (B) Davisson Germer, is correct.

Note:

De-Broglie gave an equation $\lambda = \,\dfrac{{\text{h}}}{{\text{p}}}$ where, ${\text{p}}$ is the momentum. The equation relates the momentum of a particle and wavelength of a wave. The de-Broglie wavelength of the particle is inversely proportional to its momentum. J. J. Thomson discovered that electrons are particles and his son G.P Thomson told that they are not. Rutherford discovered the nucleus. The diffraction pattern is the property of waves.