Question

3) An alpha particle can be produced in certain radioactive decays of nuclei and consists of two protons and two neutrons. The particle has a charge of q = +2e and a mass of 4.00 u, where u is the atomic mass unit, with 1 u = 1.661 × 10 2'kg. Suppose an alpha particle travels in a circular path of radius 4.50 cm in a uniform magnetic field with B-1.20 T. Calculate (a) its speed, (b) its period of revolution, (c) its kinetic energy, and (d) the potential difference through which it would have to be accelerated to achieve this energy.

Answer 1

V = rqB/m alpha = 2eBr/4u = 2(1.60 times 10^-19 c) (1.02T) (4.50 times 10^-2 m)/4 u(1.661 times 10^-27 kg/u) v = 2.60 times 10^6 m/s T = 2 pi r/v = 2pi(4.50 times 10^-2m)/2.60 times 10^6m/s = 1.087474 times 10^-7 s T = 1.09 times 10^-7 s k = 1/2 m alpha v^2 = 1/2 4u times(1.661 times 10^-27 kg/u)(2.60 times 10^6 m/s)^2 k = 2.24567 times 10^-14 J = 1.40 times 10^5 ev delta v = k/q = 1.40 times 10^5 ev/2e = 7 times 10^4 v