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

Question

An alpha particle (the nucleus of helium nucleus with charge+2e and mass 4.0u ( 1u = 1.66 x 10-27) moves in acircular orbit of radius R=12cm in a uniform magnetic field of0.25T. Where the magnetic field is perpendicular to theplane. a) the speed of the alpha particle b) the period of the circular motion c) the direction of the rotation An alpha particle (the nucleus of helium nucleus with charge+2e and mass 4.0u ( 1u = 1.66 x 10-27) moves in acircular orbit of radius R=12cm in a uniform magnetic field of0.25T. Where the magnetic field is perpendicular to theplane. a) the speed of the alpha particle b) the period of the circular motion c) the direction of the rotation

Explanation / Answer

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

Mass m = 4 u = 4 8 1.67 * 10 ^ -27 kg

Radius r = 12 cm =0.12 m

Magnetic field B = 0.25 T

In magnetic field Bvq = mv ^ 2/ r

From this speed v = Bqr / m

Plug the values weget v = 1.437 * 10 ^ 6 m / s

(b). Angular speed w = v / r

                                  = 11.976 * 10 ^ 6 rad / s

Period of the circular motion T = 2(pi) / w

                                                  = 5.246 * 10 ^ -7 s

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