1

Electromagnetic Radiation

2

3

4

c=

How many wavelengths pass through point P in one second? Frequency!

P

5

Electromagnetic Radiation

6

A radio operator broadcasts at a frequency of 14.2 MHz (megahertz).What is the wavelength of the radio waves put out by the transmitter?

ms

sm

MHz

smc

c

1.21102.14

100.3

2.14

100.316

1818

- Solve example 7.2.

- Calculate the wavelengths of the electromagnetic radiation presented in previous slide.

7

Atomic Spectra

Now, replace white light source with a hydrogen lamp.

8

H2 → 2H

H → H*(excited)

H*(excited) → H (Ground state) + light

ب

أ

عضوالةطاق

cathode

anode

Discharge tube

9

Continuous spectrum

Line spectrum

Problem: No explanation provided by classical physics.

Scientists (such as Lyman, Balmer and Paschen) analyzed the observed lineswith respect to their wavelengths. Rydberg summarized their efforts in the so-called Rydberg’s equation:

22

21

111

nnR

R=1.09678×10-2 nm-1

Rydberg’s constant

n: positive integer.

10

Calculate the wavelength, in nanometers, in the line of spectrum of hydrogenCorresponding to n1=2 and to n2=4!

lightGreen

nmnmcm

nmcm

x

mxm

nmcm

cmcm

cmcm

cmcm

nnR

3.4861010863.410863.4

101

10

10101

?1

10863.46.20564

1

6.2056416

3109678

1

16

1

4

1109678

4

1

2

1109678

1

111

755

7

7

92

51

11

122

1

22

21

11

Energy of Light- Energy of electromagnetic waves

h h h h h h h h h h

-However, Planck (Black body radiation) Einstein (photoelectric effect)

Light composed of tiny particles, called quanta (photons)

Energy of each photon (quantum) = h × Ephoton = h × Number of photons determines light intensity. h=6.6×10-34 J.s

Planck’s constant

12

Bohr’s Theory

Bohr’s Postulates:

•Electron moves in circular orbits around the nucleus.

•Electron can possess only certain energy values corresponding to the orbit.

•Electron can “jump” from one orbit to another, the energy difference will be emitted or absorbed in the form of light quanta.

13

22 1

nZAEn A=2.18×10-18 J=13.6 eV

Z : atomic numbern : positive integer = 1, 2, 3, …

14

The larger n- the larger is the orbit size, the farther is the electron from nucleus- the larger is the electron energy

Comparison to throwing stone upwards.

Negative sign means that the electron is under the influence of the nucleus.

Electron free from nucleus attracting force when n=∞.

15

Explanation of line spectrum

nlow

nhigh

Rch

A

nnch

A

c

c

nnh

A

hnn

AE

n

A

n

AEEE

highlow

highlow

highlow

lowhighlowhigh

22

22

22

22

111

11

11

16

Lyman series Balmer Series Paschen Series ends at n=1 ends at n=2 ends at n=3

UV visible Infra-red

17

Example 7.5

Calculate the energy, frequency and wavelength of the photon emitted when an electron in the hydrogen atom drops from the fifth to the second energy level.

nmms

smc

ssJ

J

h

E

JJE

nnAEE

photon

photon

highlowphoton

5.43210325.41094.6

100.3

1094.6106.6

10578.4

10578.45

1

2

11018.2

11

7114

18

11434

19

1922

18

22

18

De Broglie HypothesisLight behaves: - as waves (electromagnetic waves)

Hertz experiment

- as particles (photons) Photoelectric effect, Compton effect

Why should light be special??!!!!!

Generalization of dual nature (wave nature & particle nature) to all matter.

Any moving object can be considered to be a wave!!!

Energy of that object is E=mc2

If object considered to be a wave, E=h

De Broglie suggested:

19

p

h

vm

h

cm

h

cmh

cmc

hcmh

22

De Broglie relation De Broglie wavelength

Experimental evidence: electron diffraction Diffraction is a phenomenon that only waves can undergo Includes waves interference

20

Example: Calculate the wavelength of a football player weighing 60 kg moving in the yard with 10 km/h velocity.

mmkg

sJs

vm

h

sms

mhkmv

3534

1096.3778.260

106.6

/778.23600

10000/10

too small to be observed experimentally

Example: Calculate the wavelength of an electron moving with a velocity of 1000 km/h.

Angstrommmkg

ssJ

vm

h25.71025.7

1000000)1011.9(

106.6 1031

34

X-ray: diffraction on crystals

21

Wave mechanicsA version of quantum mechanics (modern concepts in physics)

Electron in atoms are considered to be standing waves.

Each electron in atom is described by a set of numbers called Quantum numbers.