Please help with last question

A group of students floated a charged invisible tape above another charged tape. They determined that the approximate charge on the floating tape was about 7e-09 C. The floating tape was 21 cm long and 1.875 cm wide. The ratio of the number of excess electronic charges to the number of molecules on the surface of the tape is the fraction of the molecules on the surface of the tape that have gained (or lost) an extra electronic charge e = 1.6e-19 C. What is this fraction? To estimate this, assume that molecules in the tape are arranged in a cubic lattice, as indicated in the accompanying figure, and that the diameter of a molecule in the tape is about 3e-10 m. de-10 m fraction of molecules with an extra charge = 1.0e-6 (# excess charges per molecule) The inverse of your previous answer has units of (molecules/excess charge). This can be interpreted as the ratio of (uncharged molecules) to (charged molecules). What is this number? 1/fraction = 1000000 (uncharged molecules per charged molecule) Make the assumption that the excess charges are di ly over the surface, so each excess charge is at the center of an area containing the number of surface molecules you just calculated. For example, if there were one charged molecule per 25 molecules, each charged molecule would be in the center of a square of 25 molecules, as shown in the diagram below. According to your calculations above, how far apart are the excess charges on these students' tape, measured in atomic diameters? 1000 molecular diameters apart Do your answers suggest that it is a common event or a rare event for a molecule to gain (or lose) an electron? Rare Common If the electric field at a location in air exceeds about 3e6 N/C, the air will become ionized and a spark will be triggered. In Chapter 16 we will see that the electric field in a region very close to a uniformly charged disk or plate depends approximately only on the charge per square meter (total charge Q divided by total surface area A): E = 1Q Use this model to calculate the magnitude of the electric field at a location in the air very close to your tape (less than 1 mm from the surface of the tape), and note how it compares to the electric field needed to trigger a spark in the air. E = 214094.56 > N/C This is a significant fraction of the breakdown field for air (3e6 N/C). If there were enough charge on a tape to make a field strong enough to trigger a spark, the air would become a conductor, and charge would leak off the tape. So the amount of excess charge you can put on a tape is limited by the breakdown strength of air