Which of the following is not correct about cyclotron?

Options

A. It is a machine to accelerate charged particles or ions to high energies.
B. Cyclotron uses both electric and magnetic fields in combination to increase the energy of charged particles.
C. The operation of the cyclotron is based on the fact that the time for one revolution of an ion is independent of its speed or radius of its orbit.
D. The charged particles and ions in cyclotron can move on any arbitrary path.

Explanation

To determine which statement about the cyclotron is not correct, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Cyclotron**:
- A cyclotron is a device used to accelerate charged particles (like protons, deuterons, or alpha particles) to high energies. It consists of two D-shaped electrodes (called "D's") and operates using both electric and magnetic fields.

2. **Analyzing the Options**:
- **Option A**: "It is a machine to accelerate charged particles or ions to high energies."
- This statement is **correct**. The primary function of a cyclotron is indeed to accelerate charged particles to high energies.

- **Option B**: "Cyclotron uses both electric and magnetic fields in combination to increase the energy of the charged particle."
- This statement is also **correct**. The cyclotron employs an alternating electric field to accelerate the particles and a magnetic field to keep them in a circular path.

- **Option C**: "The operation of cyclotron is based on the fact that the time for one revolution of an ion is independent of the speed and radius of its orbit."
- This statement is **correct**. The time period for one complete revolution of a charged particle in a cyclotron is indeed independent of its speed and the radius of its orbit. It depends only on the mass of the particle, the charge, and the magnetic field strength.

- **Option D**: "The charged particles and ions in cyclotron can move on any arbitrary path."
- This statement is **incorrect**. Charged particles in a cyclotron follow a circular path due to the magnetic field. They cannot move on any arbitrary path; their motion is constrained to circular trajectories.

3. **Conclusion**:
- The statement that is not correct about the cyclotron is **Option D**.

### Final Answer:
**The charged particles and ions in cyclotron can move on any arbitrary path.** (This statement is not correct.)

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