(17\%) Problem 1: An element in the periodic table may be specified as ZAEl where El is the chemical symbol, Z is its atomic number, and A is its mass number. The atomic number, Z, is the number of protons in the atomic nucleus, and it also indicates that the charge of the nucleus is +Ze where e is the fundamental charge. Protons and neutrons, collectively known as nucleons, have roughly the same mass, so the mass number, A, which is the total number of nucleons, is an indication of the mass of the atom. (The electrons contribute an insignificant amount of mass.) For lighter elements, the number of neutrons is approximately equal to the number of protons, and for elements from helium, 24He, through zinc, 43Zn, the approximation A2Z is valid to within about ten percent. The nucleus may be approximated as a sphere where the radius depends upon the total number of nucleons as RA=(1.21016m)A1/3(1.21015m)(2Z)1/3 where the approximate version is only useful for the lighter elements. A 50% Part (a) To probe the atomic nucleus, a beam of energetic protons is directed at atoms that are immobile because they are part of a metal foil or a crystal lattice. Assume that a proton approaches from a distance where it has negligible potential energy and K=2.49106eV of kinetic energy. What is the closest distance, in meters, that it may approach the nucleus of an atom with atomic number Z=21 ? Ifints! 09 o deduction per hint. Hisis remaining: 3 Feedbaeki 04 deduction per feedoack. A 50\% Part (b) Express the distance of closest approach found in Part (a) as a multiple of the nuclear nadius as given by the formula RA(1.21015m)(2Z)1/3