Homework5 - value of the angular momentum L? 7. Prove that...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
PHYS343 Spring 2007 Homework #5 Due Friday March 30,2007 COB 1. For the ground state of hydrogen, calculate the probability of finding the electron in the interval o o a 4 r a < < . 2. (a) For the ground state of the hydrogen atom, determine the radial distance for which the probability of finding the electron less than this distance is 90%. Give a numerical answer to two significant figures. (b) Repeat the calculation for a 99% probability. 3. Estimate the probability that the electron will be found inside the proton for (a) the 2s state and (b) the 2p state. Assume that a proton has a radius of approximately 1 fm. 4. (a) What are the possible values of L and Lz for the 3p state? (b) For the 3d state? 5. A hydrogen atom is in an excited state, n=5. (a) What are the possible values of the quantum numbers and m ? (b) What are the possible values of the orbital angular momentum L? 6. (a) Prove that the function ( 29 θ cos e r C ψ δ 2 r - = is a solution of the hydrogen atom, where 2 2 mke δ H = . (b) Determine the energy of the state. (c) What is the
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: value of the angular momentum L? 7. Prove that the operator for the x component of orbital angular momentum is given by ( 29 ( 29 ( 29 ( 29 + -= sin cos cos sin i L x H . 8. Consider a model of an electron as a tiny uniform sphere of size 10-18 m corresponding to the experimental limit on possible electron structure. Suppose that the electron intrinsic angular momentum is due to the spinning motion of a sphere with an angular frequency . Calculate the value of . Explain why this is a bad model of electron spin. 9. If you modeled the nucleus of hydrogen as a 1-D particle in a box with the distance between the walls of approximately 1 fm, what would be the energies of the first four states? 10. Assuming an electron is trapped in a 2-D square box whose sides are 1 nanometer. What are the energy values of the four lowest states?...
View Full Document

This note was uploaded on 01/16/2012 for the course PHYS 3343 taught by Professor Dr.danielk.marble during the Spring '11 term at Tarleton.

Ask a homework question - tutors are online