Question:
A proton and an \( \alpha \)-particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25 \( \mu \)s to make 5 revolutions, then the periodic time for the \( \alpha \)-particle would be
A proton and an \( \alpha \)-particle enter a uniform magnetic field perpendicularly with the same speed. If proton takes 25 \( \mu \)s to make 5 revolutions, then the periodic time for the \( \alpha \)-particle would be
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The periodic time for charged particles in a magnetic field increases with mass and decreases with charge.
Updated On: Apr 22, 2026
- 50 \( \mu \)s
- 25 \( \mu \)s
- 10 \( \mu \)s
- 5 \( \mu \)s
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the motion of charged particles in a magnetic field.
When charged particles such as protons and \( \alpha \)-particles enter a magnetic field perpendicular to their motion, they undergo circular motion. The periodic time (T) for a charged particle moving in a magnetic field is given by the formula: \[ T = \frac{2\pi m}{qB} \] where \(m\) is the mass of the particle, \(q\) is the charge, and \(B\) is the magnetic field strength.
Step 2: Comparing proton and \( \alpha \)-particle.
- A proton has a charge \(q_p = +e\) and mass \(m_p = m_p\). An \( \alpha \)-particle has a charge \(q_{\alpha} = 2e\) and mass \(m_{\alpha} = 4m_p\). - Since the \( \alpha \)-particle has twice the charge and four times the mass of the proton, its periodic time will be longer than that of the proton.
- The periodic time for the proton is given as 25 \( \mu \)s for 5 revolutions, which means the periodic time is 5 \( \mu \)s. The periodic time for the \( \alpha \)-particle would be: \[ T_{\alpha} = 2 \times T_{\text{proton}} = 2 \times 25 \, \mu s = 10 \, \mu s \]
Step 3: Conclusion.
The periodic time for the \( \alpha \)-particle is 10 \( \mu \)s. Thus, the correct answer is (3).
When charged particles such as protons and \( \alpha \)-particles enter a magnetic field perpendicular to their motion, they undergo circular motion. The periodic time (T) for a charged particle moving in a magnetic field is given by the formula: \[ T = \frac{2\pi m}{qB} \] where \(m\) is the mass of the particle, \(q\) is the charge, and \(B\) is the magnetic field strength.
Step 2: Comparing proton and \( \alpha \)-particle.
- A proton has a charge \(q_p = +e\) and mass \(m_p = m_p\). An \( \alpha \)-particle has a charge \(q_{\alpha} = 2e\) and mass \(m_{\alpha} = 4m_p\). - Since the \( \alpha \)-particle has twice the charge and four times the mass of the proton, its periodic time will be longer than that of the proton.
- The periodic time for the proton is given as 25 \( \mu \)s for 5 revolutions, which means the periodic time is 5 \( \mu \)s. The periodic time for the \( \alpha \)-particle would be: \[ T_{\alpha} = 2 \times T_{\text{proton}} = 2 \times 25 \, \mu s = 10 \, \mu s \]
Step 3: Conclusion.
The periodic time for the \( \alpha \)-particle is 10 \( \mu \)s. Thus, the correct answer is (3).
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