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 has a mass of 6.64 x 10-27. A horizontal beam of alpha particles is injected with a speed of 1.3 x 105 m/s into a region with a vertical magnetic field of magnitude 0.140 T. How long does it take an alpha particle to move halfway through a complete circle? t= ? s **Please be as detailed as possible with your response*** An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mass of 6.64 x 10-27. A horizontal beam of alpha particles is injected with a speed of 1.3 x 105 m/s into a region with a vertical magnetic field of magnitude 0.140 T. How long does it take an alpha particle to move halfway through a complete circle? t= ? s **Please be as detailed as possible with your response***

Explanation / Answer

The centripetal force acting on the alpha particle is F = mv^2/r The magnetic force is F = Bqv From the above two equations mv^2/ r = Bqv The radius of the circular orbit is r = (mv)/(Bq) = ((6.64*10^-27 kg)(1.3×10^5 m/s))/((0.140 T)( 2(1.6×10-19 C))) =1.92678x10^-2 m The time taken for an alpha particle to move halfway through a complete circle is t= (pr)/v = (p(1.92678x10^-2 m))/(1.3×10^6 m/s) = 4.656289x10^-8 s

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