Question

The cyclotron frequency of an electron grating in a magnetic field of $1\,{\text{T}}$ is approximately:
A. $28\,{\text{MHz}}$
B. $280\,{\text{MHz}}$
C. $2.8\,{\text{GHz}}$
D. $28\,{\text{GHz}}$

Answer 1

We use the cyclotron frequency formula and observe the given information then solve the solution. A cyclone from a flat cylindrical vacuum chamber accelerates charged particles from the core on a spiral road outward.

Complete step by step answer:
Given,
Magnetic field $= 1T$

For cyclotron,
The frequency is,

$$v = \dfrac{{{B_e}}} {{2\pi {m_e}}} \\\ = \dfrac{{1 \times 1.6 \times {{10}^{ - 19}}}} {{2\pi \times 9.1 \times {{10}^{ - 31}}}} \\\ = 28 \times {10^9}{\text{Hz}} \\\ {\text{ = 28}}\,{\text{GHz}} \\\$$

Hence, the required answer is ${\text{28}}\,{\text{GHz}}$

So, the correct answer is “Option D”.

Additional Information:
Cyclotron: In $1929 - 30$, at the University of California, Berkeley, a cyclotron is a type of particle accelerator invented by ErnestO'Lawrence and patented in $1932$. A cyclone from a flat cylindrical vacuum chamber accelerates charged particles from the core on a spiral road outward. By a static magnetic field, the particles are held in a spiral direction, accelerated by a rapidly changing electrical field (radio frequency). For this innovation, Lawrence won the Nobel Prize for Physics in $1939$. Until the $1950{\text{s}}$ when Cyclotrons had been replaced by the synchrotron, and are still used as a particle beam in physical and nuclear medicine, they have still been the most efficient particle accelerator technology. Lawrence at the University of California, Berkeley, designed the ${\text{4}}{\text{.67}}\,{\text{m}}$ (${\text{184}}\,{\text{in}}$) synchrocyclotron from ${\text{1940}}$
to ${\text{1946}}$, which was capable of accelerating protons to ${\text{730}}$ mega electron volts (e.g. mega volts). The largest cyclotron in Vancouver, British Columbia is the ${\text{17.1}}\,{\text{m}}$ (${\text{56}}\,{\text{ft}}$) multi-magnet TRIUMF Accelerator, capable of generating ${\text{500}}\,{\text{meV}}$ protons.

Cyclotron frequency: The frequency of a cyclotron or gyro frequency is the frequency of a charged particle moving in a uniform direction perpendicular to the magnetic field B (constant extent and direction).

Note:
A cyclotron is a type of compact particle accelerator generating radioactive isotopes for imaging. The cyclotron accelerates charged particles (protons) to high energy in a magnetic field with stable, non-radioactive isotopes being inserted in.