Problem: Figure 24-65 shows a simple mass spectrometer, designed to analyze and separate atomic and molecular ions with different charge-to-mass ratios. In the design shown, ions are accelerated through a potential difference, V, after which they enter a region containing a uniform magnetic field. They describe semicircular paths in the magnetic field and land on a detector a lateral distance x from where they entered the field region, as shown. Assume that there is no magnetic field in the accelerating region of the initial electric field, and no electric field in the semicircular path region. (a) With the situation shown in Figure 24-65, are the ions positively or negatively charged? Clearly explain your reasoning. (b) Derive an expression for x in terms of the other quantities: V, B, and the charge-to-mass ratio q/m. Assume that the ions start from rest at the beginning of the acceleration region. (c) If the mass spectrometer used has a potential difference of 11.5 kV in the accelerating region, and the ion being accelerated has a net charge of +2e and a mass of 95.0 atomic mass units, what must the magnetic field strength be to produce x = 8.25 cm? X X X X X X X X X X B X X X X X XX X X X X X X X X X F detector X X X X ion source Figure 24-65 Problem 34