In a cylotron, for the same values of B and R, what is the ratio of the maximum kinetic energies of alpha particles and deutrons?

Options

A. `1:1`
B. `3/2:1`
C. `2:1`
D. `3:1`

Answer

C

Explanation

In acyclotron, the maximum K.E of the ion, with magnetic field B and dee radius (R ) is given by `K_max=1/2(q^(2)B^(2)R^(2))/m` for same ` B and R,K propto q^(2)/m` Foe an `alpha` particle,`q=+2e and m-=4m_p` and for a deutron,`q=+e and m -=2m_p therefore (k_alpha)/K_d=(4e^(2))/(4m_p) xx (2m_p)/r^(2)=2`.