question_answer

Mention the significance of Davisson- Germer experiment. An \[\alpha \]-particle and a proton are accelerated from rest through the same potential difference\[\mathbf{V}\]. Find the ratio of de-Broglie wavelengths associated with them.           

Answer:

                Davisson-Germer experiment establishes the existence of matter waves of electrons. The kinetic energy gained by a charged particle when accelerated through a potential difference of V volts is given by \[\frac{1}{2}m{{\upsilon }^{2}}=qV\] or            \[{{m}^{2}}{{\upsilon }^{2}}=2mqV\] or            \[p=m\upsilon =\sqrt{2mqV}\] \[\therefore \]de Broglie wavelength, \[\lambda =\frac{h}{p}=\frac{h}{\sqrt{2mqV}}\] For the same potential difference \[\text{V}\], \[\frac{\lambda (\alpha -particle)}{\lambda (proton)}=\sqrt{\frac{{{m}_{p}}{{q}_{p}}}{{{m}_{\alpha }}{{q}_{\alpha }}}}=\sqrt{\frac{{{m}_{p}}\times e}{4{{m}_{p}}\times 2e}}=\frac{\mathbf{1}}{\mathbf{2}\sqrt{\mathbf{2}}}.\]