Download presentation

Presentation is loading. Please wait.

Published byBrandon Overly Modified over 3 years ago

1
The Hydrogen Atom

2
Model The “orbitals” we know from general chemistry are wave functions of “hydrogen-like” atoms Hydrogen-like: any atom, but it has only one electron Atomic charge Z can be anything in other words If we can understand atomic orbitals, we can use them to: Build up molecules Understand electronic spectroscopy

3
Hydrogen-Like Atom an electron the nucleus is at the origin electron is “confined” to the atom by a “spherically symmetric” potential r

4
Spherical Polar Coordinates It’s easier to study this “planetary like” models in terms of spherically polar coords. (r, ) than Cartesian coords. (x, y, z) x y z r can vary form 0 to can vary form 0 to r can vary from 0 to ∞ x = r sin( cos( y = r sin( sin( z = r cos( Cartesians to polar polar to Cartesians

5
The Schrodinger equation for the Hydrogen atom: Hydrogen Atom

6
The Schrodinger equation for the Hydrogen atom: Hydrogen Atom Luckily this splits up by separation of variables: For the Radial part of the Schrodinger equation: Gives R n,l (r)

7
Hydrogen Atom For the Angular parts of the Schrodinger equation: Gives l,m ( ) Gives m ( ) Quantum number rules for hydrogen atom: n = 1, 2, 3, 4, … l = 0, 1, 2, 3, …, n-1 m = -l, …, 0, …, l

8
Hydrogen Energies Summary Energies: Energies only depend on principle quantum number n Rydberg constant R H in J Orbital energy degeneracies: For every n, there are n-1 values of l For every value of l the are 2l+1 values of m l

9
Orbital Energies Orbital Energy in units of R H (J) 1s1s 0 2s2s 0 2p2p 01 3s3s 0 3p3p 01 -2 3d3d 01 2 RHRH …

10
Hydrogen Orbitals Summary Wave functions: n,l,m (r, ) = R n,l (r) Y l,m ( are called orbitals Orthogonalized modified associated Laguerre functions Spherical harmonic functions We used a Numerov solution to get these Tells what happens “inside” the orbital There are n-l-1 radial nodes We “Monte Carlo sampled” their probability density to look at them Text book pictures of orbitals (i.e. the outer shells) There are l angular nodes

11
Rn,l(r)Rn,l(r) n = 1 l = 0 R 1,0 (r)r 2 |R 1,0 | 2

12
Rn,l(r)Rn,l(r) n = 2 l = 0 R 2,0 (r)r 2 |R 2,0 | 2

13
Rn,l(r)Rn,l(r) n = 2 l = 1 R 2,1 (r)r 2 |R 2,1 | 2

14
Rn,l(r)Rn,l(r) n = 3 l = 0 R 3,0 (r)r 2 |R 3,0 | 2

15
Rn,l(r)Rn,l(r) n = 3 l = 1 R 3,1 (r)r 2 |R 3,1 | 2

16
Rn,l(r)Rn,l(r) n = 3 l = 2 R 3,2 (r)r 2 |R 3,2 | 2

17
Sampled Orbital Probability Densities

Similar presentations

OK

Hydrogen Atom and QM in 3-D 1. HW 8, problem 6.32 and A review of the hydrogen atom 2. Quiz 10.30 3. Topics in this chapter: The hydrogen atom The.

Hydrogen Atom and QM in 3-D 1. HW 8, problem 6.32 and A review of the hydrogen atom 2. Quiz 10.30 3. Topics in this chapter: The hydrogen atom The.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on cloud computing in healthcare Ppt on standing order medication Ppt on non biodegradable waste definition Ppt on algebraic expressions and identities for class 8 Ppt on generalized anxiety disorder Ppt on instrument landing system pictures Ppt on adjectives for grade 3 Ppt on different types of dresses in india Ppt on hindu religion history Ppt on cloud computing applications