Question

In cyclotron, the time taken by an ion to describe semicircular path in a dee is

• A. dependent on speed of ion.
• B. independent of mass of ion.
• C. independent of speed of ion and radius of circular path.
• D. dependent on radius of circular path.

Hint:

In a cyclotron, the time to complete a circular path is independent of the speed of the ion and the radius of the path. It depends only on the magnetic field and the charge-to-mass ratio of the ion.

Answer 1

The Correct Option is C

Step 1: Understanding the cyclotron motion.
In a cyclotron, the time taken to complete a semicircular path is determined by the magnetic force acting on the ion, which provides the centripetal force. The ion's time to complete the path is independent of its speed and the radius of the circular path. This is because the time is related to the frequency of revolution, which is determined by the magnetic field and the charge-to-mass ratio of the ion.

Step 2: Analyzing the options.
- (A) The time is independent of the speed of the ion, so this option is incorrect. - (B) The time is independent of the mass of the ion, so this option is incorrect. - (C) The time is independent of both the speed of the ion and the radius of the circular path. This is the correct option. - (D) The time is independent of the radius, so this option is incorrect.

Step 3: Conclusion.
The correct answer is (C), as the time to describe the semicircular path in a cyclotron is independent of the ion's speed and the radius of the path.