An alpha particle (the nucleus of a helium atom) consists of two protons and two

Question

An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons and a mass of 6.64 10-27 kg. A horizontal beam of alpha particles is injected with a speed of1.5 times 105 m/s into a region with a vertical magnetic field of magnitude 0.135 T. How long does it take for an alpha particle to move through a complete circle? Repeat part (a) for alpha particles with a speed of 3.0 times 105 m/s.

Explanation / Answer

a). magnetic force on alpha particle = q*v*B acceleartion of alpha particle = q*v*B/m => a = (2*1.602*10^-19)*1.5*10^5*0.135/(6.64*10^-27) = 9.77* 10^11 m/s^2 now, centripetal acceleration = m*v^2/r => a = m*v^2/r => 9.77*10^11 = (6.64*10^-27)*(1.5*10^5)^2/r => r = 1.53*10^-28 m time taken to move through a complete circle = distance/v => t = 2*pi*r/v = (2*3.14*1.53*10^-28)/(1.5*10^5) = 6.4* 10^-33 s b). v' = 2v = 2*(1.5*10^5) m/s a' = q*v'*B/m = 2*a = 1.95*10^12 m/s^2 now, centripetal acceleration = m*v^2/r => a = m*v^2/r => 1.95*10^12 = (6.64*10^-27)*(1.5*10^5)^2/r => r = 7.65*10^-29 m time taken to move through a complete circle = distance/v => t = 2*pi*r/v = (2*3.14*7.65*10^-29)/(3*10^5) = 1.6* 10^-33 s

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