Simple Nature - Light and Matter

12 The subatomic particles called muons behave exactly likeelectrons, except that a muon’s mass is greater by a factor of 206.77.Muons are continually bombarding the Earth as part of the streamof particles from space known as cosmic rays. When a muon strikesan atom, it can displace one of its electrons. If the atom happensto be a hydrogen atom, then the muon takes up an orbit that ison the average 206.77 times closer to the proton than the orbit ofthe ejected electron. How many times greater is the electric forceexperienced by the muon than that previously felt by the electron?√13 (a) Recall that the gravitational energy of two gravitationallyinteracting spheres is given by U g = −Gm 1 m 2 /r, where r is thecenter-to-center distance. What would be the analogous equationfor two electrically interacting spheres? Justify your choice of aplus or minus sign on physical grounds, considering attraction and√repulsion.(b) Use this expression to estimate the energy required to pull aparta raisin-cookie atom of the one-electron type, assuming a radius of10 −10 √m.(c) Compare this with the result of problem 9.14 If you put two hydrogen atoms near each other, they will feelan attractive force, and they will pull together to form a molecule.(Molecules consisting of two hydrogen atoms are the normal formof hydrogen gas.) Why do they feel a force if they are near eachother, since each is electrically neutral? Shouldn’t the attractiveand repulsive forces all cancel out exactly? Use the raisin cookiemodel. (Students who have taken chemistry often try to use fanciermodels to explain this, but if you can’t explain it using a simplemodel, you probably don’t understand the fancy model as well asyou thought you did!)15 The figure shows one layer of the three-dimensional structureof a salt crystal. The atoms extend much farther off in all directions,but only a six-by-six square is shown here. The larger circles arethe chlorine ions, which have charges of −e. The smaller circles aresodium ions, with charges of +e. The distance between neighboringions is about 0.3 nm. Real crystals are never perfect, and the crystalshown here has two defects: a missing atom at one location, and anextra lithium atom, shown as a grey circle, inserted in one of thesmall gaps. If the lithium atom has a charge of +e, what is thedirection and magnitude of the total force on it? Assume there areno other defects nearby in the crystal besides the two shown here.⊲ Hint, p. 920√Problem 15.506 Chapter 8 Atoms and Electromagnetism