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A mass spectrograph is a device for separating charged particles having different masses. Consider two particles of the same charge $q$ but different masses $m 1$ and $m 2$ injected into the region of a uniform magnetic field $B$ with a known velocity $v$ normal to the magnetic field as shown in the figure. The particles are separated by a distance $d$ , given by :

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$d = \frac{|(m_{2} - m_{1}) v|}{|q B|}$

$d = \frac{|2 (m_{2} - m_{1}) v|}{|q B|}$

$d = \frac{|(m_{2} - m_{1}) v|}{|2 q B|}$

$d = \frac{|(m_{2} - m_{1}) v|}{|4 q B|}$

answer is B.

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Detailed Solution

If $R_{1}$ and $R_{2}$ are the radii of paths of charged particles, then

$2 R_{1} + d = 2 R_{2}$ Also $R_{1} = \frac{m_{1} v}{q B}$ and $R_{2} = \frac{m_{2} v}{q B}$ ,

$d = \frac{|2 (m_{2} - m_{1}) v|}{|q B|}$

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