Lecture 17 - Quantum mechanics

Lecture 17 - Quantum mechanics - Problem Set 2 due at end...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Problem Set 2 due at end of class on Fri Feb 18 th . Midterm 1 key on website. Schrdinger Equation for Hydrogen Atom H-atom has one electron and one proton. Proton fixed and electron can move in three dimensions (x, y, z). Potential energy (V) given by coulombic interaction: ) ( 8 2 2 2 2 2 2 2 2 = + + + V E h m z y x e (x) E (x) V dx (x) d m 8 h n 2 n 2 2 2 n n = + r e Z V 2 2 4 = e- + r ) ( ) ( x E x H n n n = n=1,2,3 Energy of H-atom is Quantized Principal quantum number n determines total energy of the electron: Same as Bohr Model for the case Z = 1. n = 1, 2, 3 A e m h a e 529 . 2 2 = = Bohr radius = 2 2 18 1 1 10 179 . 2 i f n n J E e- + 3 2 1 2 2 2 4 2 1 8 n h e m Z E e n = = = 2 18 2 2 1 10 179 . 2 1 8 n J n a e E n hcR H 1 2 3 n = 4 n = 1 n = 2 n = 3 n = 4 = 2 18 1 10 179 . 2 n J E n Quantized Energy Levels of H-atom = 2 2 18 1 1 10 179 . 2 i f n n E Absorption Emission ( E = h ) 4 3 2 1 = 2 1 n hcR E H n Energy Levels of Hydrogen Emission = 2 2 18 1 1 10 179 . 2 i f n n E nm E hc 120 1 2 = = nm E hc 486 2 4 = = Wavefunction in Polar Coordinates [ ] ( ) 8 sin 1 ) / ( sin sin 1 2 2 2 2 2 2 2 2 2 = + + + + + V E h m r r r r r e e- + r...
View Full Document

Page1 / 22

Lecture 17 - Quantum mechanics - Problem Set 2 due at end...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online