1. The Bohr-Rutherford Atom
Nils
Bohr
Ernest
Rutherford

2. 1895 J.J. Thomson discovered electron
Vacuum flask
cathode
+ +
- - -
“cathode rays”
+ + - +
anode

3. Plum pudding? - - - - - - - - - Positively charged Negatively charged
porridge
Negatively charged
raisins (plums) + + + + - - - + + + + + - - - + + + + - - + + - +
10-10m

4. Planetary-like? - - - - - + Positively charged Negatively charged
dense central nucleus
Negatively charged
orbiting electrons - - - + - -
10-10m

5. Rutherford Experiment
Vacuum
flask
a-rays

6. concentrated in a dense
What’s in the box?
or is all the mass
concentrated in a dense
“ball-bearing”?
Is all the mass spread
throughout as in a box
of marshmallows”?

7. Figure it out without opening (or shaking)
Shoot bullets randomly through the box. If it
is filled with marshmallows, all the bullets will go straight through without (much) deflection

8. Figure it out without opening (or shaking)
If it contains a ball-bearing most the bullets will go straight through without deflection---but not all
Occasionally, a bullet will collide nearly head-on to the ball-bearing and be deflected by a large angle

9. no way for a-rays to scatter at wide angles
Rutherford used a-ray “bullets” to distinguish between the plum-pudding & planetary models
Plum-pudding: + + + + a - - - + + + + a + - - - + a + + + - a - + + - +
no way for a-rays to scatter at wide angles

10. distinguishing between the plum-pudding & planetary models+ a a - -
Occasionally, an a-rays will be pointed head-on
to a nucleus & will scatter at a wide angle

11. Rutherford saw ~1/10,000 a-rays scatter at wide angles+ a a - -
from this he inferred a nuclear
size of about 10-14m

12. Rutherford atom Not to scale!!! + 10-10m If it were to scale,
the nucleus would
be too small to see
10-14m +
Even though it has more than 99.9% of the atom’s mass

13. Classical theory had trouble with Rutherford’s atom
Orbiting electrons are accelerating
Accelerating electrons should radiate light
According to Maxwell’s
theory, a Rutherford
atom would only survive
for only about secs

14. Other peculiar discoveries:
sola
Other peculiar discoveries:
Solar light spectrum:
Fraunhofer discovered that some wavelengths are
missing from the sun’s black-body spectrum

15. Other discoveries… Low pressure gasses, when heated,
do not radiate black-body-like spectra;
instead they radiate only a few specific colors

16. bright colors from hydrogen match the missing colors in sunlight
Hydrogen spectrum
Solar spectrum

17. Bohr’s idea
“Allowed”
orbits

19. Hydrogen energy levels4 3 1 +

20. Hydrogen energy levels2 1 +

21. Electrons in atoms are confined matter waves ala deBroglie
However, if the circumference is exactly an
integer number of wavelengths, successive
turns will interfere constructively
This wave, as it goes around, will interfere
with itself destructively and cancel itself out
Bohr’s allowed energy states correspond to those
with orbits that are integer numbers of wavelengths

22. Bohr orbits

23. Bohr orbits

24. Quantum Mechanical Model
1920’s
Werner Heisenberg (Uncertainty Principle)
Louis de Broglie (electron has wave properties)
Erwin Schrodinger (mathematical equations using probability, quantum numbers)

25. Werner Heisenberg: Uncertainty Principle
We can not know both the position and momentum of a particle at a given time.

26. Louis de Broglie, (France, 1892-1987) Wave Properties of Matter (1923)
Since light waves have a particle behavior (as shown by Einstein in the Photoelectric Effect), then particles could have a wave behavior.
de Broglie wavelength
l= h mv

27. Electron Motion Around Atom Shown as a de Broglie Wave

28. Davisson and Germer (USA, 1927) confirmed de Broglie’s hypothesis for electrons.
Electrons produced a diffraction pattern similar to x-rays.

29. Quantum Mechanics
Erwin Schrodinger
Schrodinger’s equation

30. Erwin Schrodinger, 1925 Quantum (wave) Mechanical Model of the Atom
Four quantum numbers are required to describe the state of the hydrogen atom.

31. Matter waves are “probability” waves
Probability to detect the
electron at some place
is  y2 at that spot y
Electrons will never be detected here
Electrons are most likely
to be detected here
or here

32. Quantum mechanical atom
Bohr’s original idea
Probability density
Quantum Mechanics

33. Different QM states of the H atom