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 kg. 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

Answer is not 4.6x10-8!

**Please be as detailed as possible with your response***

Explanation / Answer

As soon as the alpha particle (q = 2e) enters the magnetic field, it will experience a force: F = qvB that is also centripetal F = m(v^2/r) So m(v^2/r) = qvB --> v = qrB/m Using the definition of speed: v = d/t, we can calculate time: t = d/v For half a circle d = pi * r, so t = (pi * r)/v = (pi * r)/(qrB/m) = pi m/qB t = pi (6.64 x 10-27 kg)/ ((2 * 1.6 x 10-19 C) * 0.140 T) t = 4.7 x 10-7 s

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