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A cyclotron is used to accelerate proton...

A cyclotron is used to accelerate protons, deuterons, `alpha`-particles, etc. If the energy attained, after acceleration, by the protons is E, the energy attained by `alpha`-particles shall be

A

4 E

B

2 E

C

E

D

E/4

Text Solution

Verified by Experts

The correct Answer is:
C
`K = (1)/(2) mv^(2) = (q^(2) B^(2) R^(2))/(2m) implies K prop (q^(2))/(m)`
`implies (E_(p))/(E_(alpha)) = ((e)/(2e))^(2) xx (4m)/(m) implies E_(p) = E_(alpha) = E`.
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The cyclotron is a device which is used to accelerate charged particles such as protons, deutrons, alpha particles, etc. to very high energy. The principle on which a cyclotron works is based on the fact that an electric field can accelerate a charged particle and a magnetic field can throw it into a circular orbit. A particle of charge +q experiences a force qE in an electric field E and this force is independent of velocity of the particle. The particle is accelerated in the direction of the magnetic field. On the other hand, a magnetic field at right angles to the direction of motion of the particle throws the particle in a circular orbit in which the particle revolves with a frequency that does not depend on its speed. A modest potential difference is used as a sources of electric field. If a charged particle is made to pass through this potential difference a number of times, it will acquire an enormous by large velocity and hence kinetic energy. Cyclotron is not suitable for accelerating

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