In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by

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 $\left(\frac{	ext { charge on the ion }}{	ext { mass of the ion }}ight)$ will be proportional to\

Professor PC Thomas Classes · Answer

(a) : In mass spectrometer when ions are accelerated through potential $V$, $$ \frac{1}{2} m v^{2}=q V 	ag{i} $$ where $m$ is the mass of ion, $q$ is the charge of the ion. As the magnetic field curves the path of the ions in a semicircular orbit\ $	herefore B q v=\frac{m v^{2}}{R} \Rightarrow v=\frac{B q R}{m}$\ Substituting (ii) in (i), we get $$ \frac{1}{2} m\left[\frac{B q R}{m}ight]^{2}=q V $$ or, $\frac{q}{m}=\frac{2 V}{B^{2} R^{2}}$\ Since $V, B$ are constants,\ $\frac{q}{m} \propto \frac{1}{R^{2}}$ or, $\frac{	ext { charge on the ion }}{	ext { mass of the ion }} \propto \frac{1}{R^{2}}$\