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Mid-Term-042709

# Mid-Term-042709 - 110A Physical Chemistry Quantum Mechanics...

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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. 1.1 If the lifetime of an excited state of an atom is 10 -9 sec., what is the uncertainty of the energy of the state? 1.2 A nucleus in an excited state with lifetime 10 -12 sec 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 0 and a , and V(x) = 0 inside the box are: E = (h 2 n 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) sin 2 (n π x/a) 2.1 What are the energies of a particle of mass m in a 1D box with walls located at 0 and 2a , and those of a particle with walls located at –a and a ? 2.2 What are the wave-functions of a particle of mass m in a 1D box with walls located at
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