EM SPECTRUM Chapter 4 EM Spectrum with Frequency and Wavelength

Definitions Wavelength: The distance from one crest to another of a wave. Frequency: The number of wavelengths that pass in 1 second.

Electromagnetic (EM) Spectrum The EM Spectrum is the range of all possible wave frequencies of electromagnetic radiation, waves created by the systematic interactions of oscillating electric and magnetic fields The general term for all electromagnetic radiation is light The range of EM Spectrum is from very low frequency known as radio waves to very high frequency known as gamma radiation The visible spectrum of light is in the center portion of this EM Spectrum All EM Spectrum travels at the same speed in a vacuum – this speed is known as the speed of light, 3.00 x 108 m/s

EM Spectrum Image used courtesy of http://9-4fordham.wikispaces.com/Electro+Magnetic+Spectrum+and+light

Speed of Light and Frequency Since the speed of all EM radiation is the same, there is a clear mathematical relationship between the frequency of the light and its wavelength. All waves travel at a speed that is equal to the product of its frequency (the reciprocal of time) and its wavelength (distance) c = f λ The speed of EM radiation is fixed at 3.00 x 108 m/s Therefore: 3.00 x 108 m/s = f λ Speed of light = frequency x wavelength As frequency increases, wavelength decreases. As wavelength increases, frequency decreases. Example: If frequency doubles, wavelength is cut in half!

As f ↑, λ↓: Calculations If the wavelength of a radio wave is 15.0 meters, what is its frequency? c = f λ 3.00 x 108 m/s = f (15.0 m) (3.00 x 108 m/s) / 15.0 m = f 2.00 x107 s-1 = f Frequency = 2.00 x107 Hertz If the frequency of gamma radiation is 6.25 x 1022 Hertz, what is its wavelength? 3.00 x 108 m/s = (6.25 x 1022 s-1) λ (3.00 x 108 m/s) / (6.25 x 1022 s-1) = λ 4.80 x10-15 m = λ Wavelength = 4.80 x10-15 m

Key Terms Emission spectrum- The range of all possible wave frequencies of electromagnetic radiation. Wavelength- The distance from one crest to another of a wave. Frequency-The number of wavelengths that pass in 1 second.

UV Light and Skin Cancer UV light has been associated with skin cancer Violet light does not cause cancer. Ultraviolet radiation has a higher frequency than violet light. Therefore the photons have greater energy. This greater energy can damage cells of the skin.

ENERGY

As frequency increases, the energy of the wave increases. Planck’s Law Max Planck determined in 1900 there was a mathematical relationship between the energy of EM radiation and the frequency of that radiation: As frequency increases, the energy of the wave increases. E = h f Energy = Planck’s constant x frequency E = (6.63 x 10-34 Joule seconds) f

Planck’s Law Calculations Example: If the wavelength of green light is 5.21 x 10-7 meters, what is the energy of this light? E = h f 3.00 x 108 m/s = f (5.21 x 10-7 m) (3.00 x 108 m/s) / 5.21 x 10-7 m = f 5.76 x1014 s-1 = f Frequency = 5.76 x1014 Hertz E = (6.63 x 10-34 Joule seconds) (5.76 x1014 s-1) E = 3.82 x10-19 Joules

Planck’s Law Equation with Speed of Light E = h f C = f λ If the speed of light equation is rearranged to solve for frequency it is: f = c/λ If f = c/λ, then c/λ can replace f in Planck’s Law Equation: E = h (c/λ) Energy can be found directly from wavelength using the following equation: E = h c λ

Implication of Planck’s Law & the Bohr Model In order to move an electron to a higher energy level, excite an electron, energy must be absorbed to move the electron – excitation energy. Electrons exist in fixed energy levels with a specific amount of energy. The amount of energy needed to excite the electron is a fixed amount of energy equal to the difference in the energy associated with the level the electron is moving from to the energy associated with the level the electron is moving to. When the excitation energy is removed, the electron will return to its ground state and the energy released is equal to the excitation energy. The energy released is released as light. Result - every element has a unique spectra of light associated with it and the spectra can be used to identify the element

Excitation Energy

Key Terms Photoelectric effect- Quantum- Planck’s constant-As frequency increases, the energy of the wave increases Photon- Ground state- Excited state- Line-emission spectrum- Continuous spectrum-