A mass spectrometer is a device which selelct particle of equal mass. An ion with an electric charge `qgt0`. Starts at rest from s ource S and is accelerated through a potential difference V. it passes thorugh a hole into a region of constant magnetic field `vecB` perpendicular to the plane of the paper as shown in the figure. The particle is deflected by the magnetic field and emerges thorugh the bottom hole at a distance d from the top hole. The mass of the particle is:

Options

A. `(qBd)/(V)`
B. `(qB^(2)d^(2))/(4V)`
C. `(qB^(2)d^(2))/(8V)`
D. `(qBd)/(2V)`

Answer

C

Explanation

Radius `r=(d)/(2)" "=(mv)/(qB)`
Alsl `qV=(1)/(2)mv^(2)" or "v=sqrt((2qV)/(m))`
`:. (d)/(2)=(m(sqrt((2qV)/(m))))/(qB)`
or `m=(qB^(2)d^(2))/(8V)`