An alternating electric field of frequency \(\nu\), is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons(mass=m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by:

1. \(\mathrm{B}=\frac{m \nu}{\mathrm{e}}\) and \(K=2 m \pi^{2} \mathrm{\nu}^{2} \mathrm{R}^{2}\) $\frac{}{}\mathrm{}{\mathrm{}}^{\mathrm{}}{\mathrm{}}^{\mathrm{}}{\mathrm{}}^{\mathrm{}}$

2.$\frac{\mathrm{}\mathrm{}}{}{}^{\mathrm{}}{}^{\mathrm{}}$\(\mathrm{B}=\frac{2\pi m \nu}{\mathrm{e}}\) and \(K=m^2 \pi \mathrm{\nu} \mathrm{R}^{2}\)

3. ${\mathrm{}}^{\mathrm{}}$\(\mathrm{B}=\frac{2\pi m \nu}{\mathrm{e}}\) and \(K=2 m \pi^{2} \mathrm{\nu}^{2} \mathrm{R}^{2}\)

4. ${}^{\mathrm{}}$\(\mathrm{B}=\frac{m \nu}{\mathrm{e}}\) and \(K=m^2 \pi \mathrm{\nu} \mathrm{R}^{2}\)

What is the primary function of the electric field in a cyclotron?

1. energize the charged particle.

2. bring the charged particle again and again into the field.

3. cancel the force due to the magnetic field.

4. guide charged particles to the exit part.

Suppose a cyclotron is operated at an oscillator frequency of 12 MHz and a discharge radius of 53 cm. What is the resulting kinetic energy of the deuterons?
(Mass of deuteron, \(m=3.34\times10^{-27}\) kg)

1. 16.6 MeV
2. 12 MeV
3. 15 MeV
4. 14 MeV

Which of the following statements about cyclotron is correct?