A mass spectrometer is a tool used to determine accurately the mass of individual ionized atoms or molecules, or to separate atoms or molecules that have similar but slightly different masses. For example, you can deduce the age of a small sample of cloth from an ancient tomb, by using a mass spectrometer to determine the relative abundances of carbon-14 (whose nucleus contains 6 protons and 8 neutrons) and carbon-12 (the most common isotope, whose nuceus contains 6 protons and 6 neutrons). In organic material the ratio of 1"C to 12c depends on how old the material is, which is the basis for "carbon-14 dating." C is continually produced in the upper atmosphere by nuclear reactions caused by "cosmic rays" (high-energy charged particles from outer space, mainly protons), and C is radioactive with a half-ife of 5700 years. When a cotton plant is growing, some of the COz it extracts from the air to build tissue contains "C which has diffused down from the upper atmosphere. But after the cotton has been harvested there is no further intake of 4c from the air, and the cosmic rays that create C in the upper atmosphere can't penetrate the atmosphere and reach the cloth. So the amount of 14C in cotton cloth continualy decreases with time, while the amount of non-radioactive 1c remains constant. Here is a particular kind of mass spectrometer (see the figure). Carbon from the sample is ionized in the lon source at the left. The resulting singly ionized 1c* and c* ions have negligibly small initial velocities (and can be considered to be at rest). They are accelerated through the potential difference Av. They then enter a region where the magnetic field has a foxed magnitude 8= 0.18 T. The lons pass through electric defiection plates that are 1 cm apart and have a potential difference AV2 that is adjusted so that the electric deflection and the magnetic deflection cancel each other for a particular isotope: one isotope goes straight through, and the other isotope is deflected and misses the entrance to the next section of the spectrometer. The distance from the entrance to the fixed ion detector is a distance of w- 22 cm. There are controls that let you vary the accelerating potential AV and the deflection potential AVz in order that only c* or "c* ions go all the way through the system and reach the detector. You count each kind of ion for fixed times and thus determine the relative abundances. The various defiections insure that you count only the desired type of ion for a particular setting of the two voltages. Accclerating plates AV. detector Deflection plates AV Oher isctope s deflected throurhout this region (a) Which accelerating plate is positive? left O right Which deflection plate is positive? top O bottom What is the direction of the magnetic field inside the spectrometer? O out of page into page (b) Determine the appropriate numerical values of AV; and Av, for c. Carry out your intermediate calculations algebraically, so that you can use the algebraic results in the next part. AV - AVz - (c) Determine the appropriate numerical values of AV, and AV for c. AV: