Question

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 ion/ mass of ion) will be: (a) 1/R(b) 1/R^2(c) R^2(d) R

Answer 1

Dear student

$$\begin{gathered} 1)workdoneoncharge=qV \\ kineticenergyaquiredisK=qV \\ \frac{1}{2}m{v}^2=qV \\ v=\sqrt{\frac{2qV}{m}} \\ Radiusoftheparticleis \\ R=\frac{mv}{Bq} \\ R=\frac{m}{Bq}\times \sqrt{\frac{2qV}{m}}=\frac{1}{B}\sqrt{\frac{2mV}{q}} \\ {R}^2=\frac{2mV}{B^{2}q} \\ \frac{q}{m}=\frac{2V}{B^2{R}^2} \\ so\frac{q}{m}isproportionalto{R}^{-2} \\ Regards \end{gathered}$$