Question

A cyclotron has frequency f and energy E. If the energy is doubled, frequency becomes

• A. f
• B. 2f
• C. $\frac{f}{2}$
• D. 4f

Hint:

This energy-independence is precisely the principle that allows cyclotrons to work effectively with an alternating voltage of a constant fixed frequency!

Answer 1

The Correct Option is A

A cyclotron is a type of particle accelerator that is used to accelerate charged particles using a magnetic field and an electric field. The frequency of a cyclotron, denoted by \(f\), is determined by the magnetic field and the charge-to-mass ratio of the particle being accelerated.

To understand why the frequency does not change with energy, let's consider the cyclotron frequency formula:

\(f = \frac{qB}{2\pi m}\)

where:

• \(q\) = charge of the particle
• \(B\) = magnetic field strength
• \(m\) = mass of the particle

The cyclotron frequency \(f\) is independent of the energy \(E\) of the particles. This is because the frequency is dependent only on the charge, the magnetic field strength, and the mass of the particles, none of which change as the particle gains energy in a cyclotron.

Therefore, when the energy is doubled, the frequency remains constant.

Let's analyze the options:

• \(f\) - Correct, as the frequency does not change with variations in energy.
• \(2f\) - Incorrect, as there is no relation in the cyclotron setup that causes the frequency to double when energy is doubled.
• \(\frac{f}{2}\) - Incorrect, for similar reasons; the frequency is not halved.
• \(4f\) - Incorrect, as neither the frequency quadruples when energy is doubled.

In conclusion, the cyclotron frequency \(f\) remains unchanged when the energy is doubled because it is independent of the energy. The correct answer is \(f\).