A steady beam of alpha particles ( q = + 2 e )traveling with constant kinetic en

Question

A steady beam of alpha particles (q = + 2e)traveling with constant kinetic energy 18 MeV carries a current of 0.30 µA. (a) If the beam is directed perpendicular to aplane surface, how many alpha particles strike the surface in 3.0s?
1

(b) At any instant, how many alpha particles are there in a given20 cm length of the beam?
2

(c) Through what potential difference was it necessary toaccelerate each alpha particle from rest to bring it to an energyof 18 MeV?
3 V (a) If the beam is directed perpendicular to aplane surface, how many alpha particles strike the surface in 3.0s?
1

(b) At any instant, how many alpha particles are there in a given20 cm length of the beam?
2

(c) Through what potential difference was it necessary toaccelerate each alpha particle from rest to bring it to an energyof 18 MeV?
3 V

Explanation / Answer

q = 2e, K = 16 MeV, I = 0.30 A = 0.30 C/s, m =4*1.67*10-27 kg, L = 20 cm a) during every second, the number is N I = Nq N = I/q = 9.375*1011 /s during 3.0 second, the number is 3.0*9.375*1011 =3.125*1012 b) speed v = (2K/m) = 2.77*107 m/s t = L/v number = N*t = NL/v = 6.77*103 c) qV = K V = K/(2e) = 8 MV = 8*106 V

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