Light - LIGHT Light Light has wave-like characteristics....

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Unformatted text preview: LIGHT Light Light has wave-like characteristics. Emitted light depends upon the object’s temperature. Light has particle-like characteristics. The motion of a light source affects wavelengths. The t t Th structure of atoms explains why each chemical element f t l i h h h i l l t emits and absorbs light at specific wavelengths. Wave-like Characteristics Wavelength: Distance between successive crests (λ). 1 nm = 10-9 m 1 Å = 0.1 nm = 10-10 m Frequency: F Number f N b of crests th t pass a specific point in t that ifi i ti one second (ν or f). Speed: Frequency times Wavelength (c) c = λ ν = 3 x 105 km/s Example Yellow Light ν = 6.0 x 1014 /s c = νλ so λ = c/ν = (3 x 108 m/s) / (6.0 x 1014 /s) = 5 0 x 10-7 m (6 0 5.0 Propagation of Light Apparent Brightness Flux = Luminosity / 4 π d2 Inverse Square Law Flux Fl 1 4 π d22 d22 --------- = ----------- = -----Flux2 4 π d12 d12 Measuring the Speed of Light Olaus Roemer (1675) timed when moons disappeared in to Jupiter s shadow. Jupiter’s shadow Eclipses were retarded when y Earth was far away. Showed light did not travel infinitely fast. Did not know the Earth-Sun id k h hS distance, so he could not p p g compute the speed of light. Measuring the Speed of Light Jean Foucault (1850) used a rapidly rotating mirror. One O must measure the h deflection angle and know the p g speed of the rotating mirror. Accuracy was better than 1%. Modern Value c = 299,792.458 km/s Visible Light Visible or Optical Light Range from 700 nm (Red) to 400 nm (Violet) White light is a combination of these colors. Newton’s experiment proved that p p prisms do not add color. Electromagnetic Spectrum Wavelength Ranges Gamma X-rays Ultraviolet Visible Infrared Microwave Radio wave 0.01 0 01 nm 0.01 to 20 nm 20 to 400 nm 400 to 700 nm 700 nm to mm mm to cm cm to km Example FM Radio Station ν = 94.9 MHz = 94.9 x 106 /s c = νλ so λ = c/ν = (3 x 108 m/s) / (94.9 x 106 /s) = 3 2 m (94 9 3.2 Light Light has wave-like characteristics. Emitted light depends upon the object’s temperature. Temperature Effects Temperature determines the type of electromagnetic radiation emitted. Temperature is a measure of the average motion of the gas molecules. Electromagnetic radiation is emitted when El i di i i i d h electric charges accelerate – that is, whenever they change either the speed or the direction of their motion. Each motion collision results in the emission of radiation. Color Indicates Temperature Temperature Scales Kelvin Temperature Scale Coldest Temperature = 0 K (no atomic motion) No negative temperatures No degree symbol – just K [The Mechanical Universe #45] Blackbodies Consider an idealized object that absorbs all the light that impinges on it. Such an it object is called a blackbody. A blackbody absorbs the entire energy incident upon it and heats up until it is emitting energy at the same g gy rate that it is being absorbed. Are stars blackbodies? Blackbody Radiation A blackbody with a temperature higher than absolute zero emits some energy in all wavelengths. A blackbody at higher temperature emits more energy at all wavelengths than does a cooler one. Blackbody Curves Blackbody Radiation A blackbody with a temperature higher than absolute zero emits some energy in all wavelengths. A blackbody at higher temperature emits more energy at all wavelengths than does a cooler one. The higher the temperature, the shorter the wavelength at which the maximum energy is emitted. emitted Blackbody Curves Wien’s Law The wavelength of maximum energy is given by Wien’s Law λ max = 0 0029 / T 0.0029 (where λmax is in meters and T is temperature) Examples: Sun λmax = 500 nm = 5.0 x 10-7 m T = 0.0029 / 5.0 x 10-7 = 5,800 K Rigel λmax = 240 nm = 2 4 x 10-7 m 2.4 T = 0 0029 / 2.4 x 10-7 = 12 000 K 0.0029 2 4 12,000 Stefan-Boltzmann Law Total energy is provided by the Stefan-Boltzmann Law: E = A σ T4 E = 4 π R2 σ T4 (σ is equal to 5.670 x 10-8 joule/m2) Stefan-Boltzmann Law Example: E = 4 π R2 σ T4 ERigel / ESun = (RRigel / RSun)2 (TRigel / TSun)4 = (50 / 1)2 (12,000 / 5,800)4 = (2500) (18) = 45,000 X PRS Question 1. The Star Betelgeuse has a temperature of 3000 K and the Sun’s temperature is about 6000 K. Assuming the Radii are the same, what is the ratio of energies of Betelgeuse to the Sun? a. 0.50 d. 16 b. 2.0 e. 0.06 c. c 3000 Light Light has wave-like characteristics. Emitted light depends upon the object’s temperature. Light has particle-like characteristics. Photoelectric Effect Einstein (1905) analyzed the Photoelectric Effect. He assumed that light can be considered a stream of photons. Each photon has an energy equal to: E = hν = hc/λ h = 6.625 x 10-34 J s Photoelectric Effect Example 1) λ = 500 nm = 500 x 10-9 m E = h c / λ = (6.625 x 10-34 Js)(3 x 108 m/s) / (500 x 10-9 m) ( )( ) ( ) = 3.975 x 10-19 J ( / 1.6 x 10-19 J/eV) = 2.5 eV 2) λ = 0.2 nm = 0.2 x 10-9 m ( )( ) ( ) E = h c / λ = (6.625 x 10-34 Js)(3 x 108 m/s) / (0.2 x 10-9 m) = 9.938 x 10-19 J ( / 1.6 x 10-19 J/eV) = 6211 eV Light Light has wave-like characteristics. Emitted light depends upon the object’s temperature. Light has particle-like characteristics. The motion of a light source affects wavelengths. Doppler Shift If a light source is approaching or receding from the observer, the light waves will be, respectively, crowded closer together or spread out. The Doppler effect is only produced by radial velocities. Δλ/λ=v/c v = c Δλ / λ PRS Question 2. The Star Betelgeuse is moving away from us at a speed of 300 km/s. When one observes a spectral feature created at 500 nm, it will appear to be shifted by how much? a. 0.5 nm blueward d. 5.0 nm blueward b. 0.5 nm redward e. 5.0 nm redward c. c no shift is seen Light Light has wave-like characteristics. Emitted light depends upon the object’s temperature. Light has particle-like characteristics. The motion of a light source affects wavelengths. The t t Th structure of atoms explains why each chemical element f t l i h h h i l l t emits and absorbs light at specific wavelengths. Atomic Structure What do spectral lines tell us about the structure of atoms? After all, each element has its own unique set of spectral lines. Solar Spectrum Fraunhofer (1814) Shined sunlight through a prism and highly magnified the spectrum. He saw 600 dark lines. spectrum lines Spectra of Different Elements ...
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