Question

An \( \alpha \) particle of energy 10 eV is moving in a circular path in a uniform magnetic field. The energy of proton moving in the same path and same magnetic field will be [mass of \( \alpha \) particle = 4 times mass of proton]

• A. 4 eV
• B. 8 eV
• C. 16 eV
• D. 10 eV

Hint:

When comparing the energies of particles in a magnetic field, the energy is proportional to the mass of the particle.

Answer 1

The Correct Option is C

Step 1: Kinetic energy of charged particles in a magnetic field.
The energy of a charged particle moving in a magnetic field is given by: \[ E = \frac{1}{2} mv^2 \] where \( m \) is the mass and \( v \) is the velocity.
Step 2: Relationship between mass and energy.
Since the mass of the \( \alpha \) particle is 4 times the mass of the proton, the velocity of the \( \alpha \) particle will be slower, but the energy is proportional to the mass. Thus, the energy of the proton will be four times that of the \( \alpha \) particle.
Step 3: Conclusion.
The energy of the proton will be \( 4 \times 10 \, \text{eV} = 16 \, \text{eV} \), so the correct answer is (C).