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  4. In a mass spectrograph, an ion X of mass number 24 and charge +e and another ion Y of mass number 22 and charge +2 e enter in a perpendicular magnetic field with the same velocity. The ratio of the radii of the circular path in the field will be

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Q. In a mass spectrograph, an ion $X$ of mass number 24 and charge $+e$ and another ion $Y$ of mass number 22 and charge $+2 e$ enter in a perpendicular magnetic field with the same velocity. The ratio of the radii of the circular path in the field will be

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Solution:

As, $r=\frac{m v}{q B}$ i.e., $r \propto m / q$
So, $\frac{r_{1}}{r_{2}}=\frac{m_{1}}{m_{2}} \times \frac{q_{2}}{q_{1}}$
$=\frac{24 \times 2 e}{22 \times e }=\frac{24}{11}$