Question

2. We have used the Heisenberg Uncertainty Relation to estimate a minimum energy of a confined particle. For each of the cases below, compare the Heisenberg estimate to the results of the Schroedinger Wave Equation; use the first energy level of the particle in an infinite well. Note that both of the examples below use classical energy relations (after all, the SWE is non- relativistic). a) An electron confined to 1 A (about the size of an atom). b) A proton confined to 10 fm (about the size of a nucleus).

Answer 1

(a)Energy of electron in an infinite squarewell potential, n2h n 8ma in n h state E, a=size of an atom=1.0A m-electron mass-9.le-31kg h 6.626e 34J.s for first energy level,n-1, we plug the values in hand, while using the relation => El-6.0247e-01 8 J b)if proton confined towidth a-10e-15m m, mass of proton-1.6726e-027 a-10e-15m h-6.626e -34J.s n h energy of first energy state E 3.28 Ile-0121