The ratio of the de Broglie wavelength of a particle to that of an electron is $1.813\times {10}^{-4}$. The mass of the particle, if it moves three times faster than the electron is: $\left(m_{\mathrm{e}}=9.1\times {10}^{-31}\mathrm{ }\mathrm{kg}\right)$

In the Davisson-Germer experiment, nickel crystal acts as 

A proton and an electron are accelerated by the same potential difference. Let ${\mathrm{\lambda }}_{\mathrm{e}}$ and ${\mathrm{\lambda }}_{\mathrm{p}}$ denote the de Broglie wavelength of the electrons and the proton respectively.