A mass spectrograph is used to measure the mass es of ions, orto separate ions of different masses (Section 27.5). In onedesign for such an instrument, ions with mass m and charge q areaccelerated through a potential difference V. They then entera uniform magnetic field that is perpendicular to their velocityand are deflected in a semicircular path of radius R. Adetector measures where the ions complete the semicircleand fromthis it is easy to calculate R. A) Derive the equationfor calculating the mass of the ion from measurements of B, V, R, and q. B) What potential difference V isneeded so that singly ionized 12C atoms will have R=50.0cm in a 0.150 T magnetic field? C) Suppose the beamconsists of a mixture of 12C and 14Cions. If V and B have the same values as in part (b),calculate the separation of these two isotopes at thedetector. Do you think that this beam separation issufficient for the two ions to be distinguished? (Make theassumption described in Problem 27.63 for the masses of theions.)