• The shorter the wavelength (), the higher the frequency ().

• Energy of the wave increases as frequency increases.

Electromagnetic spectrum

Converting from wavelength ( to frequency ( Converting from wavelength ( to frequency (

Ex: What is the frequency of a 400 nm EM wave?

= c/ = (3.00 x 108 m/s) / (4.00 x 10-7 m) = 7.50 x 1014 Hz

c =

Ground state: electron is at its lowest possible energy level

++

n = 1

n = 2

n = 3n = 4n = 5

Excited state: electron is above the lowest possible energy level

H1

1Photon absorbed

Photon emitted

HydrogenHydrogen

Atomic emission spectrum of hydrogen

Bohr atomic orbit

Quantum number

Orbit radius (nm)

Atomic energy level

Relative Energy

First n = 1 0.0529 1 E1

Second n = 2 0.212 2 E2 = 4E1

Third n = 3 0.476 3 E3 = 9E1

Fourth n = 4 0.846 4 E4 = 16E1

Fifth n = 5 1.32 5 E5 = 25E1

Sixth n = 6 1.90 6 E6 = 36E1

Seventh n = 7 2.59 7 E7 = 49E1

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For emission: E = Ehigher – Elower = Ephoton = h = hc/

= frequency (Hz) h = Planck’s constant (6.63 x 10-34 J·s)

= wavelength (m) c = speed of light (3.00 x 108 m/s)

Examples

1. What is the energy of a green photon having a wavelength of 514 nm?

E = hc/ = (6.626 x 10-34 J·s)(3.00 x 108 m/s)

5.14 x 10-7 m

= 3.87 x 10-19 J

2. What is the frequency of the photon in #1?

= c/ = (3.00 x 108 m/s) / (5.14 x 10-7 m) = 5.84 x 1014 Hz

3. What is the frequency of a photon that has an energy of 3.31 x 10-27 J?

= E/h = (3.31 x 10-27 J) / (6.626 x 10-34 J·s) = 5.00 x 106 Hz

(use c = )

(use E = h)

Some people say I have a dual personality!

Hi, I’m a photon!

Wave nature of light

Diffraction: the bending of waves around an object

Diffraction around an obstacle

Diffraction through an opening

Diffraction around a corner

The amount of diffraction that occurs depends upon the size of the obstacle or opening and the wavelength of the incident wave

Electromagnetic waves

Both electrical charges and magnets have fields around them.

An electromagnetic wave is a double transverse wave that consists of both an electric and a magnetic field wave

Electromagnetic waves are transverse waves because the electric and magnetic fields vibrate in a direction perpendicular to the direction of travel.

http://lectureonline.cl.msu.edu/~mmp/kap28/PhotoEffect/photo.htm

Photoelectric Effect

e

e e

e

Na metal

V

‘Particles’ of light are called photons

If light can have characteristics of BOTH particles and waves…

…can particles of matter also behave like waves?

mvh

De Broglie’s equation

h = 6.63 x 10-34 J·s

m = mass in kg

v = velocity in m/s

6.0 x 1024 kg2.8 x 104 m/s

e

9.1 x 10-31 kg3.0 x 108 m/s

5.7 x 10-2 kg53 m/s

(Venus Williams, 1998)

h = 6.63 x 10-34 J·s

m = mass in kg

v = velocity in m/smvh

What is the wavelength of these three ‘particles’?