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

Question

Quantrex Academy · Accepted Answer

Correct answer: B. 2

The maximum kinetic energy of a particle in a cyclotron is given by

K = \dfrac{q^2 B^2 R^2}{2m}

.

For an

\alpha

particle, charge

q_{\alpha} = 2e

and mass

m_{\alpha} = 4m_p

.

K_{\alpha} = \dfrac{(2e)^2 B^2 R^2}{2(4m_p)} = \dfrac{4e^2 B^2 R^2}{8m_p} = \dfrac{e^2 B^2 R^2}{2m_p}

For a deuteron, charge

q_d = e

and mass

m_d = 2m_p

.

K_d = \dfrac{e^2 B^2 R^2}{2(2m_p)} = \dfrac{e^2 B^2 R^2}{4m_p}

The ratio of their maximum kinetic energies is:

\dfrac{K_{\alpha}}{K_d} = \dfrac{\dfrac{e^2 B^2 R^2}{2m_p}}{\dfrac{e^2 B^2 R^2}{4m_p}} = \dfrac{4}{2} = 2

Answer:

2

In a cyclotron, for the same values of B and R, what is the ratio...

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