Chapter 9 1

OutlineReading: Livingston, Chapter 9

Hydrogen Atom Potential Energy Levels of a Hydrogen Atom Energy Levels for One Electron Atoms and Neutral Atoms

Chapter 9 2

Hydrogen Atom: Potential Profile

EVm

=+ 22

2

Chapter 9 3

A Quick Review of Spherical Coordinates

Chapter 9 4

Hydrogen Atom Energy Levels

eV6.138 2222

4

nnhmeEo

n ==

eV1-16.13 22

=

if nnh

With high voltage applied (similar to fluorescent lights)

Chapter 9 5

Energy Levels for Other Single Electron Atoms

rZerV

o4)(

2

=

eV)6.13(8 2

2

222

42

nZ

nhmeZE

on ==

Energy Levels for Other Neutral Atoms

Li3+

Li3+reZ

rVo

eff

4)(

2

=

eV)6.13(

8 22

222

42

nZ

nhmeZ

E effo

effn ==

Chapter 9 6

Solutions to the S.E. for Hydrogen Atom

EVm

=+ 22

2

rerV

o4)(

2

=

Chapter 9 7

Restrictions on Quantum Numbers

n = 1, 2, 3,.l = 0, 1, 2, 3,, (n-1)m = -l,, -2, -1, 0, 1, 2,, +l

s = +1/2 or -1/2

Chapter 9 8

n l m sAllowable states in subshell

Allowable states in complete

shell

1 0 0 +/- 2 22 0 0 +/- 2

81 -1 +/-

60 +/- 1 +/-

3 0 0 +/- 2

18

1 -101

+/- +/- +/-

6

2 -2-1012

+/- +/- +/- +/- +/-

10

Chapter 9 9

Shapes of Subshells

Chapter 9 10

Chapter 9 11

n = 1

n = 2

n = 3

n = 4

Chapter 9 12

Review Questions

1. Qualitatively what is the potential profile associated with a hydrogen atom? How does it relate to radius?

2. What are the allowed energy levels for a hydrogen atom? How does energy related to principal quantum number?

3. What are the allowed energy levels for a one-electron atom (not necessarily hydrogen)?

4. What are the allowed energy levels for neutral atoms? Why?5. How many unique quantum numbers an electron have according to

Paulis Exclusion Principle? 6. What are the general shapes of the subshells?7. What is the principal quantum number and subshell in 1s2? How

many electrons are in this atom? If this is a neutral atom, which one is it?

8. How are the Schrodinger Equation and the Periodic Table related?

Chapter 9 13

Important Equations

rerV

o4)(

2

=

dtdiV

m

=+ 22

2 EV

m=+ 2

2

2

eV6.138 2222

4

nnhmeEo

n == nm0528.04 2

2

==

mea oo

eV1-16.13 22

=

if nnh

rZerV

o4)(

2

= eV)6.13(

8 22

222

42

nZ

nhmeZE

on ==

n = 1, 2, 3,.l = 0, 1, 2, 3,, (n-1)m = -l,, -2, -1, 0, 1, 2,, +l

s = +1/2 or -1/2

reZ

rVo

eff

4)(

2

= eV)6.13(

8 22

222

42

nZ

nhmeZ

E effo

effn ==