Which of the following is the correct expression for cyclotron frequency?

CONCEPT:

Cyclotron:

• A cyclotron is a device used to accelerate positively charged particles (like α-particles, deuterons, etc.) to acquire enough energy to carry out nuclear disintegration, etc.
• It is based on the fact that the electric field accelerates a charged particle and the magnetic field keeps it revolving in circular orbits of constant frequency.

• A cyclotron is a type of particle accelerator. In which a perpendicular magnetic field is applied to the plane of motion of the particle which makes the particle to move in a circular path.

Magnetic force = centripetal force

Bqv = mv²/r

\(\frac{Brq}{m}\) = v

Now ω × r = v

\(ω \times r =\frac{Brq}{m}\)

\(ω = \frac{Bq}{m}\)

Now 2πV_C = ω 

\(2\pi \mathrm{V}_{\mathrm{C}} = \frac{Bq}{m}\)

\(\mathrm{V}_{\mathrm{C}} =\frac{qB}{2\pi m}\)

Hence the correct option is option 1)

Additional Information Applications of the cyclotron 

1. Cyclotrons can be used in particle therapy to treat cancer, using the ion beams from cyclotrons can be used to penetrate the body and kill tumors by radiation damage.
2. Cyclotrons can also be used to change the nuclear structure.
3. Scientists use cyclotrons for nuclear physics experiments in which they use accelerated charged particles to bombard atomic nuclei.