In a medical research facility, a beam of deuterons and a beam of alpha particles are used for hadron therapy. To achieve identical spatial resolution, both beams are adjusted so that the particles have the same de Broglie wavelength. The deuterons in their beam travel at a speed of 1.25×105 m s−11.25 \times 10^5 \text{ m s}^{-1}1.25×105 m s−1.
Calculate the speed of the alpha particles in their beam.
Take the mass of a deuteron to be 3.34×10−27 kg3.34 \times 10^{-27} \text{ kg}3.34×10−27 kg and the mass of an alpha particle to be 6.64×10−27 kg6.64 \times 10^{-27} \text{ kg}6.64×10−27 kg.
