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Which of the follwing particles will ha...

Which of the follwing particles will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field?

A

Electron

B

Proton

C

`He^(+)`

D

`Li^(++)`

Text Solution

AI Generated Solution

The correct Answer is:
To determine which particle will have the minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field, we need to analyze the motion of charged particles in a magnetic field. ### Step-by-Step Solution: 1. **Understanding the Motion of Charged Particles in a Magnetic Field**: When a charged particle moves in a magnetic field, it experiences a magnetic force that acts perpendicular to both the velocity of the particle and the magnetic field. This force causes the particle to move in a circular path. 2. **Formula for the Radius of Circular Motion**: The radius \( R \) of the circular path of a charged particle in a magnetic field is given by the formula: \[ R = \frac{mv}{qB} \] where: - \( m \) is the mass of the particle, - \( v \) is the velocity of the particle, - \( q \) is the charge of the particle, - \( B \) is the magnetic field strength. 3. **Frequency of Revolution**: The frequency \( f \) of revolution of the particle is related to the radius of the circular path. It can be expressed as: \[ f = \frac{qB}{2\pi m} \] This shows that the frequency is inversely proportional to the mass of the particle \( m \). 4. **Comparing Proton and Electron**: - The mass of a proton \( (m_p) \) is significantly greater than the mass of an electron \( (m_e) \). - Since both particles are projected with the same velocity \( v \) and are subjected to the same magnetic field \( B \), we can conclude that the particle with the greater mass will have a lower frequency of revolution. 5. **Conclusion**: Since the proton has a greater mass than the electron, it will have a lower frequency of revolution when both are projected with the same velocity perpendicular to the magnetic field. Therefore, the particle with the minimum frequency of revolution is the **proton**. ### Final Answer: The particle that will have the minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field is the **proton**.
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