The Sine Wave Mathematically, a function that represents a smooth oscillation For example, if we drew the motion of how the weight bobs on the spring to the weight we would draw out a sine wave.
The Sine Wave You commonly see waves in the environment Light Sound Electricity Ocean waves
The Sine Wave The wavelength of a wave refers to the distance between two crests of troughs. Units of wavelength are based off the meter.
The Sine Wave The frequency of a wave represents the number of wavelengths that pass a fixed point in a second Units of frequency are in hertz (hz)
Electromagnetic Waves Electromagnetic waves consist of two components, an electric and a magnetic wave. Both are at right angles (90 degrees) from each other.
Electromagnetic Waves Electromagnetic waves travel at 3.00x10 8 meters per second. This is also known as the speed of light. At this speed, an electromagnetic wave can go around the Earth 8 times in one second.
Electromagnetic Waves This does not mean you can t slow an electromagnetic wave down. In a vacuum, electromagnetic waves travel at the speed of light. They slow down considerably if they are passing through a medium.
Electromagnetic Spectrum Note that radio waves have the lowest frequencies while gamma-rays have the highest frequency.
The Sine Wave Mathematically, the relationship between wavelength and frequency are as follows: c = v λ Speed of Light (3.00x10 8 m/s) Frequency (hz) Wavelength (in meters)
The Sine Wave What is the wavelength of yellow sodium emission, which has a frequency of 5.09x10 14 hz? c = 3.00x10 8 m/s c = v λ = unknown λ = 3.00x10 8 m/s (5.09x10 14 hz) (λ) v = 5.09x10 14 hz λ = 5.89 x 10-7 m
The Sine Wave What is the frequency of violet light with a wavelength of 4.08x10-9 meters? c = 3.00x10 8 m/s c = v λ = 4.08x10-9 m λ = 3.00x10 8 m/s (v) (4.08x10-9 m) v = unknown v = 7.35x10 16 hz
Relationship Between Energy and Frequency Mathematically, the relationship between energy and frequency are as follows: E = h v Energy (in joules) Planck s Constant (6.626x10-34 Jxs) Frequency (in hz)
Relationship Between Energy and Frequency A red spectral line has a frequency of 4.47x10 14 hz. Calculate the energy of one photon of this light. E = unknown h = 6.626x10-34 J x s v = 4.47x10 14 hz E = h E = v (6.626x10-34 J x s) (4.47x10 14 hz) E = 2.96x10-19 J
Relationship Between Energy Frequency, and Wavelength Mathematically, the relationship between energy and frequency are as follows: E = h v You can substitute frequency between the two equations! c = v λ
Relationship Between Energy and Frequency A red spectral line has a wavelength of 6.71x10-7 meters. Calculate the energy of one photon of this light. c = v λ E = unknown h = 6.626x10-34 J x s v = unknown λ = 6.71x10-7 m c = 3.00x10 8 m/s = 3.0x10 8 m/s (v)(6.71x10-7 m) v = 4.47x10 14 hz E E E E = h v = (6.626x10-34 J x s) (v) = = (6.626x10-34 J x s) (4.47x10 14 hz) 2.96x10-19 J
Relationship Between Energy and Frequency An electromagnetic wave has an energy of 3.15x10-19 J. What is the wavelength of this wave? c = v λ E = 3.15x10-19 J h = 6.626x10-34 J x s v = unknown λ = unknown c = 3.00x10 8 m/s = 3.0x10 8 m/s (4.75x10 14 hz) (λ) λ = 6.32x10-7 m E = h v 3.15x10-19 J = (6.626x10-34 J x s) (v) 3.15x10-19 J = (6.626x10-34 J x s) (v) v = 4.75x10 14 hz
Electrons and Light Think back to electron orbitals. Electrons found in orbitals have a particular energy level. However, if energy (namely in the form of photons of light) strike an electron, it can jump to a higher energy level Think of this like throwing a ball straight upwards. The more energy you use to throw a ball, the higher it can go.
Electrons and Light However, an electron can not permanently stay in its excited state. The electron will return back to the ground state after emitting a photon of energy. If this photon of energy is within the wavelength and frequency of our vision, we see the emission of photon as a form of light
Lasers We use this principle of electrons to invent lasers (which is an acronym for light amplification by stimulated emission of radiation) However in lasers, we selectively choose which frequency and wavelength of light we want emitted
De Broglie s Equation The scientist Louis de Broglie discovered the relationship between wavelength, frequency, and mass. Planck s Constant (6.626x10-34 J x s) Wavelength (in meters) Mass (in kg) Speed (in m/s)
De Broglie s Equation We can use De Broglie s equation to determine the wavelength, mass, or frequency for matter assuming we have two of the three variables. For example, calculate the wavelength of a wave associated with a 1.00kg mass moving at 0.278m/s λ = unknown λ = h = 6.626x10-34 J x s v = 0.278 m/s m = 1.00 kg h m v 6.626x10 λ = -34 J x s 1.00kg x 0.278 m/s λ = 2.38 x 10-33 m
De Broglie s Equation Calculate the wavelength associated with an electron traveling at a speed of 2.19x10 6 m/s with a mass of 9.11x10-31 kg. λ = unknown λ = h = 6.626x10-34 J x s v = 2.19x10 6 m/s m = 9.11x10-31 kg h m v 6.626x10 λ = -34 J x s 9.11x10-31 kg x 2.19x10 6 m/s λ = 3.32 x 10-10 m
The Visual Spectra
Visible Light Visible light represents the colors that we are able to see with our eyes. The color with the shortest wavelength and the highest frequency is violet while the color with the longest wavelength and the lowest frequency is red. And the order of colors, from longest wavelength to shortest, is red, orange, yellow, green, blue, indigo, and violet.
Photon emissions generated by electrons in the excited state ultimately give each element a specific atomic spectra In a sense, each element has a unique visual fingerprint Atomic Spectra
Prisms And if you have a prism, you can force light into its component colors.
The Doppler Shift Planetary Bodies Start Here You Are Here