Particles as waves and Light as

particlesChapter 6 part II

Energy is Quantized Energy can only occur in

discrete units of size hv. Each packet is called a

quantum. Energy can only be

transferred in whole quanta. Energy seems to have

particle like behavior.

Photons

Einstein proposed that electromagnetic radiation is quantized.

This light can be viewed as a stream of particles.

Each particle is a photon, with energy of:

Ephoton=hv=hc/

Theory of Relativity Einstein went on to

propose this: E=mc2

Energy has mass!!!

If E=mc2 and E=hc/…Then m = (E/c2) Ephoton = hc

Substitute hc for E

Then m= (E/c2) = (hc/ ) = h

c2 c This means that a photon appears to have mass!

The dual nature of light

Compton working with x-rays and electrons seems to have proved this.

Energy is quantized. Electromagnetic

radiation once thought to act only as waves, seems to also have the characteristics of particles.

Can matter have wave-like characteristics?

Louis de Broglie de Broglie solved the problem of the

wavelike behavior of a particle. Then m= h

(velocity v) Then solving for we get h

mv This is called de Broglie’s equation.

For example:

Compare the wavelength of an electron (m=9.11x10-31kg) traveling at a speed of 1.0x107m/s with that of a baseball (m=0.10kg) traveling at 35 m/s

Answer:=h/ mv h= 6.626 x 10-34 Js 1 J= 1kg m2/s2

For electron = 6.626 x 10-34 (kgmm)/s (9.11x10-31 kg)(1.0x107m/s)Answer: 7.27 x 10-11m

And the Ball??

1.9x10-34m

Atomic Spectrum of Hydrogen When light is passed through a prism

one gets an emission spectrum. When all wavelengths are possible

one gets a continuous spectrum. When energy is quantized the

spectrum is a line spectrum, or discrete.

Light & Electromagnetic Radiation The light spectrum is continuous. All the wavelengths of light may pass.

The hydrogen emission spectrum: Is discrete. This indicates only certain energies are allowed

for the electron in the hydrogen atom.

Hydrogen is discrete as the energy of electrons are quantized.

∆E =hv= hc/ is the wavelength of light emitted. Since the line is discrete only certain

energies are possible for the hydrogen electron.

The Bohr model: Bohr’s quantum model proposed that

electrons in a hydrogen atom move around the nucleus in certain allowed circular orbits.

Bohr’s equation Z is the nuclear charge n is an integer representing the orbital,

larger n= larger radius n=1 is the ground state