An alpha particle is composed of 2 protons and 2 neutrons, equivalent to the nuc

Question

An alpha particle is composed of 2 protons and 2 neutrons, equivalent to the nucleus of a helium atom. However, the aplha particle has no electrons so its mass is slightly less than that of a helium atom (malpha = (6.645 X 10-27)kg < mhelium). Suppose an alpha particle has been created with a kinetic energy of (1.50 X 106) eV inside a vacuum chamber with a uniform magnetic field. If the magnetic field has a strength of 0.500 T and it is perpendicular to the velocity vector, what is the radius of curvature of the path the alpha particle follows?

Explanation / Answer

balancing forces acting on the alpha particle

Centripetal force = Magnetic force

mass of particle * (Velocity^2)/radius of curvature = Magnetic field * velocity of particle * charge of particle

radius of curvature = (mass of particle * Velocity) / (Magnetic field * charge of particle)

now, velocity = sqrt(2*kinetic energy/mass)

velocity of particle = sqrt(2*1.5*10^6*(1.9*10^(-19)/(6.645 X 10^(-27))) = 9.2*10^6 m/s

radius of curvature = (6.645 X 10-27 * 9.2*10^6) / (0.5 * 2*1.6*10^(-19)) = 0.38 m

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