# (a) State briefly, with what purpose was Davisson and Germer experiment performed and what inference was drawn from this.(b) Obtain an expression for the ratio of the accelerating potentials required to accelerate a proton and an $\alpha -$particle to have the same de-Broglie wavelength associated with them.

(a) The purpose of the Davisson Germs experiment was to verify the wave nature of the electron. It confirms the diffraction effect of electron beams from crystal.

(b) To determine the Ratio of accelerating potential:-

We know the De-Broglie wavelength

$\lambda =\frac{h}{\sqrt{2mqV}}$

Where, m = mass,

v=velocity

q = charge

h=plank's constant

charge of the alpha particle is two times the charge of the proton

$\therefore \frac{h}{\sqrt{2m_{p}eV_{p}}}=\frac{h}{2\sqrt{m_{\alpha }eV_{\alpha }}}$

mass of an alpha particle is 4 times the mass of the proton and

Hence, the ratio will be,

$\frac{V_{p}}{V_{\alpha }}=\frac{8}{1}$

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