Q129 / 200 · NEET 2007 · Physics

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:

  • Correct answer
    A
    $\frac{1}{R^2}$
  • B
    $R^2$
  • C
    $R$
  • D
    $\frac{1}{R}$

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 $\begin{aligned} & R \propto \frac{\sqrt{m q}}{q} \\ & \Rightarrow \frac{q}{m} \propto \frac{1}{R^2} \end{aligned}$

Hence, the correct answer is option: 'A'.

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