C1. In the operating room, anesthesiologists use mass spectrometers to monitor the respiratory gases of patients undergoing surgery. One gas that is often monitored is the anesthetic isoflurane (molecular mass = 3.06 10^-25 kg). In a spectrometer, a single ionized molecule of isoflurane (charge = + e) moves at a speed of 8.25 10³ m/s on a circular path that has a radius of 0.167 m. What is the magnitude of the magnetic field that the spectrometer uses?

C2. Suppose that an ion source in a mass spectrometer produces doubly ionized gold ions (Au²⁺), each with a mass of 3.27 10^-25 kg. The ions are accelerated from rest through a potential difference of 1.90 kV. Then, a 0.480-T magnetic field causes the ions to follow a circular path. Determine the radius of the path.

C3. Two isotopes of carbon, carbon-12 and carbon-13, have masses of 19.93 10^-27 kg and 21.59 10^-27 kg, respectively. These two isotopes are singly ionized (+e) and each is given a speed of 6.531 10⁵ m/s. The ions then enter the bending region of a mass spectrometer where the magnetic field is 0.6813 T. Determine the spatial separation between the two isotopes after they have traveled through a half-circle. Use 1.602 10^-19 C as the elementary charge and give your answer to four significant figures.

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