In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio (Charge on the ion/Mass of the ion ) will be proportional to

Posted: 19-08-2022

A. 1/R

B. 1/R²

C. R²

D. R

Answer:- Right option is B) 1/R²

Let q be the charge and m be the mass of the particle. Energy is amplified only by the electric field doing work.

⇒qV=21mv2⇒v=mq

2V

The magnetic field delivers receptive force for motion in circle:

⇒Rmv2=qvB

⇒v=mqBR⇒BR12V

=mq

⇒mq=B2R22V

⇒mq∝R21

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