In a mass spectrometer for measuring the masses of ions, the ions are initially accelerated by an electric…
In a mass spectrometer 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 $\left(\frac{\text { charge on the ion }}{\text { mass of the ion }}\right)$ will be proportional to:
$\frac{1}{R^2}$
$R^2$
$R$
$\frac{1}{R}$
Solution
Radius of semicircular path
$R=\frac{m v}{q B}=\frac{\sqrt{2 m q V}}{q B}$
As $V$ and $B$ are constant so
$\begin{aligned}
& R \propto \frac{\sqrt{m q}}{q} \\
& \Rightarrow \frac{q}{m} \propto \frac{1}{R^2}
\end{aligned}$