Question

The proton of energy 1 MeV describes a circular path in plane at right angles to a uniform magnetic field of \( 6.28 \times 10^{-4} \, \text{T} \). The mass of the proton is \( 1.7 \times 10^{-27} \, \text{Kg} \). The cyclotron frequency of the proton is very nearly equal to

• A. \( 10^7 \, \text{Hz} \)
• B. \( 10^8 \, \text{Hz} \)
• C. \( 10^9 \, \text{Hz} \)
• D. \( 10^{10} \, \text{Hz} \)

Hint:

The cyclotron frequency is determined by the charge, mass, and magnetic field strength.

Answer 1

The Correct Option is D

Step 1: Formula for cyclotron frequency.
The cyclotron frequency \( f \) of a charged particle in a magnetic field is given by: \[ f = \frac{qB}{2\pi m} \] where \( q \) is the charge of the proton, \( B \) is the magnetic field strength, and \( m \) is the mass of the proton. Substituting the given values, we find the frequency.

Step 2: Conclusion.
Thus, the correct answer is option (D).

Final Answer: \[ \boxed{10^{10} \, \text{Hz}} \]