Thompson’s experiment (discovery of electron)

Physics at the end of XIX Century and

Major Discoveries of XX Century

Emission and absorption of light

Spectra:•Continues spectra•Line spectra

Three problems:•“Ultraviolet catastrophe”•Photoelectric effect•Michelson experiment

1

Continues spectra and “Ultraviolet catastrophe”

4TI

Stefan-Boltzmann law for blackbody radiation:

KmT 3max 1090.2

II

Wien’s displacement law:

seV

sJh

15

34

1014.4

1063.6

Plank’s constant:

hfE

I(λ)

2

Example 2: What is the wavelength the frequency of the most intense radiation from an object with temperature 100°C?

KmT 3max 1090.2

Example 1: What is the wavelength the frequency corresponding to the most intense light emitted by a giant star of surface temperature 5000 K?

Hzmsmcf

nmmKKm1468

maxmax

63max

102.510580.0//103/

58010580.05000/1090.2

Hzmsmcf

mmKKm1368

maxmax

63max

109.31077.7//103/

77.71077.7100273/1090.2

3

Photoelectric effect

light

A

Experiment: If light strikes a metal, electrons are emitted. •The effect does not occur if the frequency of the light is too low •The kinetic energy of the electrons increases with frequency

Classical theory can not explain these results. If light is a wave, classical theory predicts:• Frequency would not matter• Number of electrons and their energy should increase with intensity

Quantum theory:Einstein suggested that, given the success of Planck’s theory, light must be emitted and absorbed in small energy packets, “photons” with energy:

hfE If light is particles, theory predicts:• Increasing intensity increases number of electrons but not kinetic energy• Above a minimum energy required to break atomic bond, kinetic energy

will increase linearly with frequency• There is a cutoff frequency below which no electrons will be emitted,

regardless of intensity 4

Photoelectric effect (quantum theory)light

A

Photons!

seV

sJh

15

34

1014.4

1063.6Plank’s constant:

hfE

max0 KWhf

0max0 hf-WKeV

-V0

V

I

Stopping potential (V0):

0min Whf

5

2max2

1max mvK

Example: The work function for a certain sample is 2.3 eV. What is the stopping potential for electrons ejected from the sample by 7.0*1014 Hzelectromagnetic radiation?

?

100.7

3.2

0

14

0

V

Hzf

eVW

eVeVHzseVeV

WhfeV

6.03.2100.71014.4 14150

00

Example: The work function for sodium, cesium, copper, and iron are 2.3, 2.1, 4.7, and 4.5 eV respectively. Which of these metals will not emit electrons when visible light shines on it?

eVHzseVW

Whf

1.3105.71014.4 14150

0min

?

105.7

0

14

W

Hzf

Copper, and iron will not emit electrons

VV 6.00

Visible light: nmnm 700400 HzfHz 1414 105.7103.2

6

The Atom

1. The Thomson model (“plum-pudding” model)

It was known that atoms were electrically neutral, but that they could become charged, implying that there were positive and negative charges and that some of them could be removed.

Later, Rutherford did an experiment that showed that the positively charged nucleus must be extremely small compared to the rest of the atom.

This model had the atom consisting of a bulk positive charge, with negative electrons buried throughout.

7

The only way to account for the large angles was to assume that all the positive charge was contained within a tiny volume – now we know that the radius of the nucleus is about 1/100000 that of the atom.

2. Rutherford’s scanning experiment and planetary model

Rutherford scattered alpha particles – helium nuclei – from a metal foil and observed the scattering angle. He found that some of the angles were far larger than the plum-pudding model would allow.

Rutherford’s (planetary) model:

8

3. Atomic line spectra (Key to the structure of the atom)

A very thin gas heated in a discharge tube emits light only at characteristic frequencies.

•An atomic spectrum is a line spectrum – only certain frequencies appear.

•If white light passes through such a gas, it absorbs at those same frequencies.

9

4. Hydrogen atomThe wavelengths of electrons emitted from hydrogen have a regular pattern:

22

111

nmR

...5,4 ;3 :seriesPaschen

,...4,3 ;2 :seriesBalmer

,...3,2 ;1 :seriesLyman

nm

nm

nm

Rydberg constant:

A portion of the complete spectrum of hydrogen:

10These lines cannot be explained by the Rutherford theory

5. The Bohr Atom

Bohr proposed that the possible energy states (stationary states) for atomic electrons were quantized – only certain values were possible. Then the spectrum could be explained as transitions from one level to another.

22

111

nmR

if EEnm

hcRhc

hf

22

11

2n

hcREn eVhcR 60.13

Example:

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12

2

min

2

E

E

H

eVeV

E

eVEEn

eV

n

hcREn

40.32

60.13

60.13

60.13

22

1min

22

nmeV

nmeV

E

hc

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12220.10

1243

20.10)1(60.13 41

12

nmeVhc 1243

11

The Bohr Atom

The lowest energy level is called the ground state; the others are excited states. 12

Example: Franck- Hertz experiment

Franck and Hertz studied the motion of electrons through mercury vapor under the action of an electric field. When the electron kinetic energy was 4.9eV or grater, the vapor emitted ultraviolet light. What was the wave length of this light?

?

9.4

eVE

nmeV

nmeV

E

hc

Ehc

hf

2509.4

1243

13