Question

The cyclotron's oscillator frequency is 10 MHz. What should be the operating magnetic field for accelerating protons?
A. 0.156T
B. 0.256T
C. 0.356T
D. 0.656T

Answer 1

Hint: Firstly we will see a cyclotron. It is a device used to accelerate charged particles like protons, deuterons and alpha particles to very high energy. In question it is given that protons are accelerated and we have to find magnetic fields. It is clear that cyclotrons oscillating frequency must be equal to frequency of revolution of protons.

Formulas used:
$f=\dfrac{Beq}{2\pi m}$

Complete step by step answer:
We know that cyclotrons oscillating frequency must be equal to frequency of revolution of protons.
$\begin{align}
  & f=\dfrac{Beq}{2\pi m} \\
 & B=\dfrac{2\pi mf}{q} \\
\end{align}$
Substituting the values in S.I unit
$\begin{align}
  & B=\dfrac{2\times 3.14\times \left( 1.67\times {{10}^{-27}} \right)\times \left( 10\times {{10}^{6}} \right)}{1.67\times {{10}^{-19}}} \\
 & =0.656T \\
\end{align}$
Hence the correct option is D.

Additional information:
Uses of cyclotron:
1. The high energy particles produced in a cyclotron are used to bombard nuclei and study the resulting nuclear reactions and hence investigate nuclear structure.
2. The high energy particles are used to produce other high energy particles such as neutrons by collisions. These fast neutrons are used in atomic reactors.
3. It is used to implant ions into solid and modify their properties and synthesise new material.
4. It is used to produce radioactive isotopes which are used in hospitals for diagnosis and treatment.

Note:
Principle of a cyclotron: A charged particle can be accelerated to very high energies by making it pass through a moderate electric field large no. of times. This can be done with the help of a perpendicular magnetic field which throws charge particles into circular motion. In a cyclotron it is the electric field which accelerates the charge particles. The magnetic field does not change the speed, it only makes the charge particles to cross the same electric field again and again by making it move along a circular path.
A large increase in the energy of a cyclotron increases the velocity to a very large extent. This throws the electrons out of step with the oscillating field.
Neutrons being electrically neutral cannot be accelerated by the cyclotron.