A research facility must accelerate both protons (mass ) and deuterons (mass )
PHYSICS · Multi-part · CBSE · Physics · Dual Nature of Radiation and Matter · Dual Nature of Radiation and Matter
Problem
A research facility must accelerate both protons (mass mp) and deuterons (mass md=2mp), each carrying a single elementary charge +e, for separate experiments. In each case the particles start from rest, and relativistic effects can be neglected.
(a) The facility first requires the two particle types to emerge from their respective accelerators with the
same speed v. Derive an expression for the ratio of the required potential differences ΔVpΔVd in terms of the particle masses.
(b) Calculate the numeric value of this ratio using the given mass relationship.
(c) When instead the two particle types are each accelerated through the *same* potential difference ΔV, determine which particle attains the greater speed. Support your conclusion with quantitative reasoning.