In a cyclotron, for the same values of B and R, what is the ratio of the maximum kinetic energies of particles and deuteron? Mass of deuteron =2m_p , charge on deuteron =+e

Step-by-step solution

The maximum kinetic energy of a particle in a cyclotron is given by K = q^2 B^2 R^2 2m . For an particle, charge q_ = 2e and mass m_ = 4m_p . K_ = (2e)^2 B^2 R^2 2(4m_p) = 4e^2 B^2 R^2 8m_p = e^2 B^2 R^2 2m_p For a deuteron, charge q_d = e and mass m_d = 2m_p . K_d = e^2 B^2 R^2 2(2m_p) = e^2 B^2 R^2 4m_p The ratio of their maximum kinetic energies is: K_ K_d = e^2 B^2 R^2 2m_p e^2 B^2 R^2 4m_p = 4 2 = 2 Answer: 2