The ratio of de Broglie wavelengths of a proton and a deuteron accelerated by potential V_p and V_d respectively, ((λ_p)/(λ_d)) is 1/2. Find V_p/V_d.

De Broglie wavelength of proton: $\displaystyle \lambda_{p}=\frac{h}{\sqrt{2 m e V_{p}}}$ De Broglie wavelength of deuteron: $\displaystyle \lambda_{d}=\frac{h}{\sqrt{2(2 m) e V_{d}}}$ $\displaystyle \frac{\lambda_{p}}{\lambda_{d}}=\frac{1}{2}=\sqrt{\frac{2(2 m) e V_{d}}{2 m e V_{p}}}$ On solving: $\displaystyle \frac{V_{p}}{V_{d}}=8$