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Physical Chemistry III

Physical Chemistry III. Examples and Exercises. Normalizing a Wavefunction. Find a normalizing factor of the hydrogen’s electron wavefunction. Function of r, using spherical coordinate. Eigen eqaution. Operator Constant Function. Show if e ax is an eigenfunction of the operator d/dx

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Physical Chemistry III

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  1. Physical Chemistry III Examples and Exercises

  2. Normalizing a Wavefunction • Find a normalizing factor of the hydrogen’s electron wavefunction Function of r, using spherical coordinate

  3. Eigen eqaution Operator Constant Function • Show if eax is an eigenfunction of the operator d/dx • Show if eax2 is an eigenfunction of the operator d/dx

  4. Orthogonal wavefunction • Both sinx and sin2x are eigenfunction of d/dx, show if sinx and sin2x are orthogonal.

  5. Expectation Value • Calculate the average value of the distance of an e- from the n of H-atom

  6. Uncertainty Principle Uncertainty in position along an axis Uncenrtianty in linear momentum • Calculate the minimum uncertainty in the position of mass 1.0 g and the speed is known within 1 mm s-1.

  7. Probability (Particle in a box) • Wave function of conjugated electron of polyene can be approximated by PAB. Find the probability of locating electron between x=0 and x=0.2 nm in the lowest state in conjugated molecule of length 1.0 nm when n=1 L=1.0 nm and l = 0.2 nm

  8. Harmonic Oscillator • Find the normalizing factor of Harmonic Oscillator wavefunction

  9. Harmonic Oscillator • The bending motion of CO2 molecule can be considered as a harmonic oscillator, find the mean displacement of the oscillator

  10. Exercises • Calculate the speed of an electron of wavelength 3.0 cm • Calculate the Brogile wavelength of a mass of 1.0 g travelling at 1.0 cm s-1 • Calculate the probability of a particle in ground state between x=4.0 and 5.0 cm in a box of 10.0 cm length • Calculate the probability of a hydrogen’s electron in ground state to be found within radius a0/2 from the nucleus

  11. Exercises • Identifiy which functions are eigenfunctions of the operator d/dx • eikx • coskx • e-ax3 • Calculate the energy separation between the levels n=2 and n=6 of an electron in a box of length 1.0 nm • What are the most likely locations of a particle in a box of length L in the state n=3?

  12. Exercises • What are the most likely locations of a particle in a harmonic oscillator well of lin the state =5 ? • Confirm that the wavefunction for the ground state of a one-dimention linear harmonic oscillator is a solution of the Schrödinger eqaution • Write down the Harmonic Oscillator wavefunction in the state n=0 and 4 • Write down the Rigid Roter wavefunction Y0,0 ,Y1,2 ,Y2,1 and Y2,-2 and calculate their energies

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