17. -12.5 points OSColPhys1 22 P018 WA My Notes Ask Your A beam of alpha partide

Question

17. -12.5 points OSColPhys1 22 P018 WA My Notes Ask Your A beam of alpha partides is fired horizontally with a speed of 2.7 105 m/s into a region where there is a vertical magnetic field of magnitude 0.510 t An alpha particle is the nucleus of a helium atom and as such, consists of two protons, two neutrons, and has a mass of 6.64 x 1027 kg. (a) Determine the length of time it will take an alpha particle to move halfway around a complete circle. (b) Does the time found in part (a) increase, decrease, or stay the same, if the speed of the alpha particle is tripled? increase decrease stay the same (c) Repeat part (a) for alpha particles with a speed of 8.1 10s m/s, Supporting Materials Physical Constants Submit Answer Save Progress

Explanation / Answer

As proton enters into magneitc field, the magnetic force on proton is equal to

centeripetal force on it.

Bqv = mv²/r

Rearrange fore velocity

v = Bqr / m ...... (1)

Here charge on Alpha particle is (q = 2 x +1.60^-19 C)

Expression for period

T = 2r / v

Substitute equation (1)

T = 2r.m / (Bqr)

T = 2m / (Bq)

T = 2 ( 6.64^-27 kg ) / (0.510 T) ( 2 x 1.60^-19C)

T = 2.56 x10^-7 s

For half way around the circle,

T/2 = 1.28 x10^-7 s = 128 ns

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From the above calculations, it is cleared that the period is

independent of speed. So, time stays the same

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(c)

As it is independent of speed, the result should be same as in part (a)

that is T/2 = 1.28 x10^-7 s = 128 ns

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