A cyclotron is used to accelerate protons, deutrons, alpha-particles,etc. The maxumum kinetic energy acquired by the accelerated protons is E. What will be the maximum K,E, acquired by the alpha-partcles if they are accelarated under the same experimental conditions?

Options

A. `E`
B. `E/2`
C. `4E`
D. `2E`

Answer

A

Explanation

The maximum K.E acquired by the ions in a cyclotron is given by `1/2mv^(2)max=(q^(2)B^(2)R^(2))/(2m)` For an `alpha` particle,q=2 xx charge on the proton=2e and mass `m_alpha=4`(mass of proton)`=4m_p` For the proton, maximum K.E`(e^(2)B^(2)R^(2))/(2m_p)=E` and for the `alpha` particle maximum K.E`((2e)^(2)xx B^(2)xx R^(2))/(2 xx 4m_p)=(e^(2)B^(2)R^(2))/((2m_p))=E` thus they acquire the same K.E.