A proton of energy is moving in a circular path in a uniform magnetic field. The energy of an alpha particle moving in the same magnetic field and along the same path will be
Explanation for the correct option:
Step 1: Given
Energy of proton,
Let be the magnetic field and be the radius of the circular path.
It is given that these are the same for both the proton and the -particle .
Step 2: Formulas used
We know that, the momentum of a particle moving in a magnetic field is,
where is the mass of the particle, is its velocity, is its charge, and is the radius of its circular path.
We also know that kinetic energy,
Step 3: Calculate the energy of -particle
The kinetic energy of the proton can be written as,
An -particle is simply the nucleus of a helium-4 () atom.
Thus the mass of the -particle is times that of the proton i.e., ( is the mass of the -particle and is the mass of the proton)
The -particle has two protons thus its charge is twice that of a proton i.e., ( is the charge of the -particle and is that of the proton).
Hence, option C is correct.