110A Physical Chemistry: Quantum Mechanics Mid Term 4/27/09, 9:00 a.m. ; allotted time: 50 minutes Problem # 1: 20 pts In addition to an uncertainty principle for position and momentum, there is one for energy (E) and time (t): the product of the uncertainty of E and t is greater than or equal to the Planck constant. 1.1If the lifetime of an excited state of an atom is 10 -9sec., what is the uncertainty of the energy of the state? 1.2A nucleus in an excited state with lifetime 10 -12sec decays and emits a γ-ray. What is the uncertainty in the energy of the γ-ray? Problem # 2: 40 pts The energies of a particle of mass m in a 1D box with walls at 0and a, and V(x) = 0 inside the box are: E = (h 2n 2)/ (8 m a 2) ; n = 1, 2, ...; h is the Planck constant The probability of finding the particle at a point x inside the box is: |Ψ(x)| 2= (2/a) sin2(nπx/a) 2.1What are the energies of a particle of mass m in a 1D box with walls located at 0and 2a, and those of a particle with walls located at –aand a? 2.2What are the wave-functions of a particle of mass m in a 1D box with walls located at
This is the end of the preview.
access the rest of the document.