Chemistry Homework: Atomic Models, Matter Waves, and Relativistic Corrections - Prof. Jorg, Assignments of Quantum Chemistry

Download Chemistry Homework: Atomic Models, Matter Waves, and Relativistic Corrections - Prof. Jorg and more Assignments Quantum Chemistry in PDF only on Docsity! Homework Assignment for CHEM 5581 J. M. Weber Office: JILA A709; Phone 303-492-7841; email: weberjm@jila.colorado.edu ________________________________________________________________________ Problem Set 2 To be returned before the end of class on Wednesday, September 10, 2008 (give to me in person or slide under office door). 1. Atomic models a) Determine the velocity of an electron in Bohr’s H atom for a quantum state n. (1 credit) b) Estimate how fast an electron in Rutherford’s H atom in the ground state (n=1) would radiate its initial kinetic energy, assuming that the electron radiates energy at the same rate as at the beginning of the process. (4 credits) c) If the nucleus of a Platinum atom were the size of the sun (r=695,000 km), what would be the radius of the electron orbit in the ground state of the Pt77+ ion? (2 credits) 2. Matter Waves In order to observe diffraction, the deBroglie wavelength of a particle must be on the order of the dimension of the obstacle it is diffracted by. Imagine a strange universe where humans have the same shape and mass as in ours, and where the velocities of everyday activity are similar to ours. In that universe, however, golf is complicated by the fact that golf balls are diffracted by the hole on the green if the ball is too slow (v<5 m/s). (Neglect the fact that if Planck’s constant were other than it is, people like us would most likely not exist, and neither would golf or athletics!) a) Estimate the magnitude of ħstrange. Typical golf balls have a mass of 45 g, and the holes have a diameter of 10 cm. (2 credits) b) In our universe, Usain Bolt (Jamaica) holds the current world record for running 100 m at 9.69 s (since this year), after beating the earlier record by Asafa Powell (Jamaica) of 9.77 s. Would it be meaningful in that strange universe to hold 100-m- races with similar time frames? Argue why or why not. Both runners weigh ca. 87 kg. (3 credits) c) A billiard ball weighs roughly 200 g, and the holes are about 65 mm wide. Assume that the velocity of the ball is ca. 1 m/s. Will it be meaningful to play billiard in the strange universe? Argue why or why not. (3 credits)