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  • In a mass spectrometer used for measuring the masses of ions are initially accelerated by an electric potential V and then made to describe semicircular path of radius R using a magnetic field B. I

In a mass spectrometer used for measuring the masses of ions are initially accelerated by an electric potential V and then made to describe semicircular path 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

Option: 1

1 / R^2


Option: 2

R^2


Option: 3

R


Option: 4

1/R


Answers (1)

best_answer

In mass spectrometer, when ions are accelerated through potential V

\frac{1}{2} m v^2-q v                     ....(i)

As the magnetic field curves the path of the ions in a semicircular orbit

B q V=\frac{m v^2}{R} \Rightarrow V=\frac{B q R}{m}

substituting (ii) in (i)

\begin{aligned} & \frac{1}{2} m\left[\frac{B q R}{m}\right]=q r \\ & \text { or } \frac{q}{m}=\frac{2 r}{B^2 R^2} \end{aligned}

Since, V and B are constants

\therefore \frac{q}{m} \propto \frac{1}{R^2} .

Posted by

himanshu.meshram

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