Paleoclimate. Climatologists can determine the past temperature of the earth by comparing...

Paleoclimate. Climatologists can determine the past temperature of the earth by comparing the ratio of the isotope oxygen-18 to the isotope oxygen-16 in air trapped in ancient ice sheets, such as those in Greenland. In one method for separating these isotopes, a sample containing both of them is first singly ionized (one electron is removed) and then accelerated from rest through a potential difference V. This beam then enters a magnetic field B at right angles to the field and is bent into a quarter-circle. A particle detector at the end of the path measures the amount of each isotope,         (a) Show that the separation ∆r of the two isotopes at the detector is given by

where m16 and m18 are the masses of the two oxygen isotopes. (b) The measured masses of the two isotopes are 2.66 × 10−26 kg (16O) and 2.99 × 10−26 kg (18O). If the magnetic field is 0.050 T, what must be the accelerating potential V so that these two isotopes will be separated by 4.00 cm at the detector?