3. [-I8 Points] One mole of iron (6 x 1013 atoms) has a mass of 56 grams, and is density is 7.87 grams per cubic centimeter, so the center-tocenter distance between atoms is 2.28 x 10'10 m. You have a long thin bar of iron, 2.7 m long, with a square cross section, 0.14 cm on a side. You hang the rod vertically and attach a 204 kg mass to the bottom, and you observe that the bar becomes 1.38 cm longer. From these measurements, it is possible to determine the stiffness of one interatomic bond in iron. Top of wire 0 o " 0 ' 3 Bottom of wire 1) What is the spring stiffness of the entire wire, considered as a single macroscopic (large scale), very stiff spring? ks = E m 2) How many side-by-side atomic chains (long springs) are there in this wire? This is the same as the number of atoms on the bottom surface of the iron wire, Note that the crosssectional area of one iron atom is (2.28 x 10'1\")2 m2. Number of side-by-side long chains of atoms = 3) How many interatomic bonds are there in one atomic chain running the length of the wire? Number of bonds In total length = l: 4) What is the stiffness of a single interatomic "spring"? k5,,- = l: N/m An interatomic bond in iron is stiffer than a slinky, but less stiff than a pogo stick. The stiffness ofa single interatomic bond is very much smaller than the stiffness of the entire wire. Additional Material: ID aBook