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ProblemSet4 - Chem 120A Problem Set 4 Out Due April 7 2006...

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Chem 120A Problem Set 4 Out: March 22, 2006; Due: April 7, 2006 IN CLASS 1. a) In the infrared spectrum of H 79 Br, there is an intense line at 2630 cm - 1 . Calculated the force con- stant of H 79 Br and the period of vibration of H 79 Br. b) The force constant of 79 Br 79 Br is 240 N · m - 1 . Calculated the fundamental vibrational frequency and zero-point energy of 79 Br 79 Br c) Calculate the average z component of angular momentum, h L z i , for an electron in a ring of constant potential when it has the wavefunction: i ) ψ ( φ ) = r 1 π sin3 φ and ii ) ψ ( φ ) = r 1 2 π e - 3 i φ . 2. The Earth (mass = 6 × 10 24 kg) rotates about the sun (at an average distance of r = 1 . 5 × 10 11 m) once per year (one year = 10 π million seconds). a) What is the Earth’s angular momentum with respect to the sun in units of ¯ h ? b) What is the smallest principle quantum number n that allows the electron in a hydrogen atom to have this value of angular momentum? c) How large is such an atom? Use h ˆ r i for the H atom in the 1 s state to express this size.
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