A mass spectrometer is a device which select particle of equal mass. An ion with electric charge q > 0 and mass m starts at rest from a source S and is accelerated through a potential difference V. It passes through a hole into a region of constant magnetic field $\vec{B}$ perpendicular to the plane of the paper as shown in the figure. The particle is deflected by the magnetic field and emerges through the bottom hole at a distance d from the top hole. The mass of the particle is

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$\frac{qBd}{2 V}$

$\frac{{qB}^{2} d^{2}}{4 V}$

$\frac{{qB}^{2} d^{2}}{8 V}$

$\frac{qBd}{8 V}$

answer is C.

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Detailed Solution

$Kinetic Energy KE = Vq \Rightarrow \frac{P^{2}}{2 m} = Vq$

$\Rightarrow (Bqr)^{2} = Vq 2 m [∵ r = \frac{mV}{Bq}]$

$B^{2} q^{2} {(\frac{d}{2})}^{2} = Vq 2 m \Rightarrow m = \frac{B^{2} d^{2} q}{8 V}$

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