Week 09 Wavelength, Frequency, and Energy of Photons PDF

Light’s Wave Nature  Wave Nature of Light Electromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space. Examples: sunlight, microwaves, x-rays radio and television waves  Characteristics of Waves Wavelength (λ – lambda) – the...

Light’s Wave Nature  Wave Nature of Light Electromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space. Examples: sunlight, microwaves, x-rays radio and television waves  Characteristics of Waves Wavelength (λ – lambda) – the shortest distance between the same points on a wave; usually measure in meters, centimeters, or nanometers Frequency (f)– the number of waves that pass a given point per second; 1 Hertz equals 1 wave per second (1/s or s -1) Amplitude is a waves height from origin to crest  Speed of Light All electromagnetic waves travel at the speed of light in a vacuum and this value is a very important constant c = 3.00 x 108 meters per second (m/s) The speed of light is related to wavelength and frequency by the following equation: c = wavelength x frequency or c=λf λ = c/f f = c/λ  Using the Equation c=λf Looking at the equation, you can see that wavelength and frequency are inversely related, so as one increases the other decreases and vice versa.  Light and the Visible Spectrum Sunlight or white light is made up of a continuous range of wavelengths and frequencies. Passing sunlight through a prism show you all the color of the visible spectrum When passing through a prism, the short wavelengths bend more than the long ones, resulting in the sequence of colors ROY G BIV (red, orange, yellow, green, blue, indigo, violet)  Calculations Because all electromagnetic radiation travels at the same speed (speed of light), we can use the formula c = λ f to calculate wavelength and frequency any wave. Remember c = speed of light!  Two Formulations l = c/f f = c/l E = hc/l E = hf l is wavelength (m) C is the speed of light (3 x 108 m/s) f is frequency (1/s) (Hz) E is energy of a photon (joule) h is Planck’s constant: 6.626 x 10-34 J.s  f = c/l = 6.12x 1014 Hz  f = c/l = 2.61x 1018 Hz Calculate the wavelength of an electromagnetic wave that has a frequency of 7.8 x 106 Hz. l = c/f Calculate the Energy of an electromagnetic wave that has a frequency of 7.8 x 106 Hz. E = hc/l E = hf h= 6.626 x 10-34 J.s c= 3 x 108 m/s E = hf E = 6.626 x 10-34 J.s x 7.8 x106 /s = 5.17 x 10-27 J Calculate the Energy of an electromagnetic wave that has a wavelength of 300 nm E = hc/l E = hf h= 6.626 x 10-34 J.s c= 3 x 108 m/s nm = 10-9 m E = hc/l = 6.626 x 10-19 J  Lets Investigate the units n: nano = 10-9 1nm = 10-9 m m: micro = 10-6 1mm = 10-6 m m: mili = 10-3 1mm = 10-3 m k : kilo = 103 1 km = 103m M: mega= 106 1Mm = 106m Calculate the Energy of an radio wave that has a frequency of 100 kHz. E = hc/l E = hf h= 6.626 x 10-34 J.s c= 3 x 108 m/s 100 kHz = 100 x 103 Hz E = hf E = 6.626 x 10-34 J.s x 100 x 103 /s => E = 6.626 x 10-29 J  Quantum? A quantum is the minimum amount of energy that can be gained or lost by an atom; so matter can gain or lose energy only in small, specific amounts. So how does that relate to energy levels in an atom? Ground State vs. Excited State The ground state of an electron is the lowest energy level possible for that electron. It’s comfortable there. By adding energy, like heat or light, electrons can be exited and move up to a new energy level – they would then be in an “excited state”. This “excited state” is very uncomfortable for the electron, it wants to be back home in its ground state energy level, so it loses the energy it gained (the quantized amount) and begins to drop back down to its lowest energy level (kind of like stepping down a ladder). Sometimes the energy it loses can be seen as colors of light because the frequency of the energy is in the “visible light” range.”  Photons A photon is a particle of electromagnetic radiation (like visible light) with no mass that carries a quantum of energy. So basically, it’s a package of electromagnetic radiation with a set amount of energy. Photons can travel at different wavelengths and frequencies, so we interpret that as different colors of light. (remember, visible light can have different wavelengths and frequencies that we see as different colors!) Bohr’s Model  We can use this equation to relate the amount of quantum energy to the actual frequency of the radiation. E = hf = hc/l E is the quantum energy or a photon’s energy, h is Planck’s constant (6.626 x 10-34 J · s), f is the frequency  Practice 1. What is the energy for the following type of radiation? 6.32 x 1020 s-1 2. Use the Electromagnetic Spectrum to determine the type of radiation described in problem #1.