Light and Quantized Energy Essential Question: How would you use the formula c=lv and E=hv in wave calculations?

Wave Nature of Light?

Parts of a wave peak wavelength amplitude trough

Characteristics of Waves Wavelength ( λ ) – shortest distance between 2 equivalent points on a continuous waves (from crest to crest or from trough to trough) Units of wavelength: Usually in meters (100), Centimeters (10-2) or Nanometers (10-9)

Comparing Wavelengths Which wave has a longer wavelength? Which wave has the shorter wavelength? long wavelength crest Wavelength Wavelength trough short wavelength

Characteristics of Waves Frequency ( v ) – number of waves that pass a given point per second Units of frequency: waves per second 1 / s = s -1 = Hertz

So which type of wave has a higher frequency……one with a long wave length or one with a short wavelength Wave A Wave B Wave C

Another way to look at Frequency These 2 waves are traveling at = speeds… more crests cross the ‘finish line’ in a matter of one min.? which wave will have low frequency = long wavelength high frequency = short wavelength

Characteristics of a Wave Amplitude – wave’s height from the origin of the wave to the crest or from the origin to the trough origin

Vocab & Symbols Speed of light (c) – constant number, 3.00 x 108 m/s Wavelength ( λ ) – shortest distance between 2 equivalent points on a continuous waves; measured in m Frequency ( v ) – number of waves that pass a given point per second; measured in Hz Energy (E) – energy of the photon as it travel; measured in Joules, J Planck’s Constant (h) – constant number, 6.626 x 10-34 J . s

Wave Calculations c = λ v All electromagnetic waves travel at the speed of light in a vacuum Speed of light (c) = 3.00 x 108 m/s Speed of light is equal to product of wavelength and frequency c = λ v Rearrange to solve for wavelength or frequency. Remember speed of light (c) is a constant, always the same number

Wave Calculations Practice Calculate the υ of a wave that has a wavelength of 5.00 x 10-6 m. What is the λ of radiation with a frequency of 1.50 x 1013 Hz?

Units What units of wavelength are needed? What do you have to do if you are given a wavelength of nm?

Particle Nature of Light?

Photoelectric Effect Electrons are emitted from a metal’s surface when light with a certain frequency hits the surface

Photoelectric Effect Frequency and energy do not accumulate on the metal’s surface Specific threshold needed to be reached before the electron would be emitted

Dual Nature of Light Explains the photoelectric effect Albert Einstein proposed that light has wavelike and particle like properties Photon – massless particle that carries a quantum of energy Ephoton = hv

Energy Calculations All energy is a multiple of Planck’s Constant, a quantum of action in quantum mechanics h = 6.626 x 10-34 J . s Quantum – minimum amount of energy that can be gained or lost by an atom Planck stated that there was a relationship between the energy of a quantum and the frequency of the radiation

Schrodinger Wave Equation

Energy Calculations Energy of a photon is calculated by the multiple of Planck’s constant by frequency E = h v Rearrange to solve for energy or frequency. Remember Planck’s constant (h) is always the same number

Energy Calculations Practice Calculate the E of a wave that has a frequency of 7.66 x 1014 Hz . What is the υ of radiation with 8.35 x 10-18 J of energy?

De Broglie Equation Proposed light had both wave and particle like characteristics Therefore all moving particles have wave characteristics λ = h/mv Wavelength = λ Planck’s constant = h = 6.626 x 10-34 Mass of the particle = m Velocity = v

Using BOTH Formulas What is the energy of a 9.3 x 10-3 m wave? What is the wavelength of a 1.528 x 10-13 J wave?

Heisenberg Uncertainty Principle States it is impossible to know the velocity and the position of a particle at the same time. This is due to the fact that in order to determine the original location of an electron it would have to be hit with a high energy photon to “move” it to the new location, and therefore determine original location. However, by “hitting” it with the high energy particle would cause the original energy & wavelength to change, so the data would not be accurate.