The figure shows a mass spectrometer in which negatively charged particles of di

Question

The figure shows a mass spectrometer in which negatively charged particles of different masses enter a region through a slit and travel perpendicular to a uniform magnetic field (pointing out of the page). The particles are accelerated through the same potential difference, ?V, before entering the spectrometer and are measured by a detector when they strike the bottom wall. If a particle with charge ?Q and mass M hits the bottom wall a distance d from the slit, at what distance will a particle with charge ?4Q and mass 4M hit the bottom wall?

Explanation / Answer

mv2/2 = QV

=> v = (2QV/m)1/2

Also, QvB = mv2/r

=> r = mv/QB = [(m2/Q2B2) * (2QV/m)]1/2 = [(2V/B2)(m/Q)]1/2

=> d = 2r = [(8V/B2)(m/Q)]1/2

So, -4Q charge and 4M mass will land at the same spot as -Q charge and M mass since the ratio of mass to charge is same.

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