An alpha particle (the nucleus of helium nucleus with charge+2e and mass 4.0u (1

Question

An alpha particle (the nucleus of helium nucleus with charge+2e and mass 4.0u (1 u = 1.66E-27) moves in a circular orbit ofradius R=12 cm in a uniform magnetic field of 0.25 T, where themagnetic field is perpendicular to the orbit plane. Find: a. the speed of the particle b. the period of the circular motion An alpha particle (the nucleus of helium nucleus with charge+2e and mass 4.0u (1 u = 1.66E-27) moves in a circular orbit ofradius R=12 cm in a uniform magnetic field of 0.25 T, where themagnetic field is perpendicular to the orbit plane. Find: a. the speed of the particle b. the period of the circular motion

Explanation / Answer

Charge q= 2e = 2 * 1.6 * 10 ^ -19 C

Mass m = 4u = 4 * 1.67 * 10 ^ -27 kg

Magnetic field B = 0.25 T

Radius R = 12 cm = 0.12 m

In magnetic field Bvq = mv ^ 2/ R

From this speed v = BqR / m

                              = 1.437 * 10 ^ 6 m / s

Angular speed w = v / R

                            = 11.97 * 10 ^ 6 rad ./ s

So, period T = 2(pi) / w

                    = 5.246 * 10 ^ -7 s

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