Alpha particles (charge = +2e,mass = 6.68 × 10^-27 kg)are accelerated in a cyclotron to a final orbit radius of 0.30 m.The magnetic field in the cyclotron is 0.80 T.The period of circular motion of the alpha particles is closest to: A)0.16 μs B)0.25 μs C)0.33 μs D)0.40 μs E)0.49 μs

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Quizplus · Accepted Answer

The period of circular motion of a charged particle in a magnetic field is given by:T = 2πr/vwhere r is the radius of the orbit, v is the speed of the particle, and q is the charge of the particle.We can find the speed of the alpha particle using the centripetal force equation:mv²/r = qvBwhere m is the mass of the alpha particle, v is the speed of the alpha particle, r is the radius of the orbit, q is the charge of the alpha particle, and B is the magnetic field strength.Solving for v, we get:v = qBr/mSubstituting this expression for v into the equation for the period, we get:T = 2πr/(qBr/m)Simplifying, we get:T = 2πm/(qB)Plugging in the given values, we get:T = 2π(6.68 × 10^-27 kg)/(2e)(0.80 T)T ≈ 0.16 μsTherefore, the period of circular motion of the alpha particles is closest to 0.16 μs.

Alpha Particles (Charge = +2e,mass = 6