An electron of mass m_e and a proton of mass m_p are moving with the same kinetic energy at non-relativistic speeds. The de Broglie wavelengths associated with the electron and the proton are λ_e and λ_p respectively.

Which of the following correctly gives the ratio $\frac{{{\lambda _{\rm{e}}}}}{{{\lambda _{\rm{p}}}}}$?

A. $\frac{{{m_{\rm{p}}}}}{{{m_{\rm{e}}}}}$

B. $\frac{{{m_{\rm{e}}}}}{{{m_{\rm{p}}}}}$

C. $\sqrt {\frac{{{m_{\rm{p}}}}}{{{m_{\rm{e}}}}}}$

D. $\sqrt {\frac{{{m_{\rm{e}}}}}{{{m_{\rm{p}}}}}}$

C