Question

An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mass of 6.64×10−27kg. A horizontal beam of alpha particles is injected with a speed of 1.3×105m/s into a region with a vertical magnetic field of magnitude 0.180 T . A) How long does it take for an alpha particle to move halfway through a complete circle? B) If the speed of the alpha particle is doubled, does the time found in part A increase, decrease, or stay the same? C) Repeat part A for alpha particles with a speed of 2.6×105m/s.

Part A IP An alpha particle (the nucleus of a helium atom) consists of two protons and two neutrons, and has a mas alpha particles is injected with a speed of 1.3 × 105 m/s into a region with a vertical magnetic field of magnitude 0.180 T How long does it take for an alpha particle to move halfway through a complete circle? s of 6.64 x 10-27kg. A horizontal beam of Submit My Answers Give Up Part B If the speed of the alpha particle is doubled, does the time found in part A increase, decrease, or stay the same? O increase O decrease O stay the same Submit My Answers Give Up Part C Repeat part A for alpha particles with a speed of 2.6 × 105 m/s

Answer 1

(A) Magnetic force (Bqv) provides the centripetal force (mv²/r)
Bqv = mv²/r .. .. v = Bqr / m .. .. (q = 2 x +1.60*10^-19 C)
If T = periodic time .. T = 2πr / v
T = 2πr.m / (Bqr)
T = 2πm / (Bq) = 2π x 6.64*10^-27kg / (0.180T x [2 x 1.60*10^-19C]) =7.24*10^-7 s

►½T = 3.62*10^-7 s

(B) From T = 2π.m / (Bq) in part (A) .. T is independent of v, ►so T unchanged

(C) From part (A) .. T = 2π.m / (Bq) ... same values used as in (A) .. same answer for T