1 / 12

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

phuoc
Télécharger la présentation

Physical Chemistry III

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related