Block 4 Astronomy - Fundamentals of spectrum

Planck’s Radiation Law

1. WCW 9/232. Note- wave properties3. Turned as classwork Notes EM

spectrum4. Notes-Temp in universe,

Wien/Stephen-Boltzmann5. WCW 10/16. Turned in as classwork Notes

IDRDP

Warm-up 9 / 23 / 13

Name three different forms of ‘Light” Electromagnetic Radiation.

Critical Thinking

1. In each of the following pairs, circle the form of radiation with the LONGER WAVELENGTH:a. Red light or blue light b. Microwaves or Radio wavesc. Infrared radiation or red light d. gamma rays or UV radiation

2. In each of the following pairs, circle the form of radiation with the GREATER FREQUENCY:a. Yellow light or green light b. X-rays or gamma raysc. UV radiation or violet light d. AM radio waves or FM radio waves

3. In each of the following pairs, circle the form of radiation with the LOWER ENERGY:a. Red light or Blue light b. Microwaves or Radio wavesc. Infrared radiation or Red light d. Gamma rays or UV radiatione. Yellow light or Green light f. X-rays or gamma raysg. UV radiation or Violet light h. AM radio waves or FM radio waves

4. Springfield’s “Classic Rock” radio station broadcasts at a frequency of 102.1 MHz. Whatis the length of the radio wave in meters?

5. A beam of light has a wavelength of 506 nanometers. What is the frequency of the light?What color is the light?

6. Blue light has a frequency of 6.98 x 1014 Hertz. Calculate the wavelength of blue light innanometers.

Wrap-up

5. When sodium is heated, a yellow spectral line whose energy is 3.37 x 10-19 J/photon is produced.a. What is the frequency of this light?b. What is its wavelength?

Notes wave properties

Radiation– Radiation is emitted by all matter– EM radiation was “wave-like” characteristics– EM waves are oscillating electrical and magnetic fields– Oscillating electrical field produces an oscillating magnetic field and vice-versa– Frequency of oscillation has wide range

– Speed of propogation (v), frequency (f) and wavelength (λ) are related

v = f λExamples from the board

300,000 km per second = 3 x 108 m/s

Properties of a wave:

Wavelength- Lambda, λ units- m, meters, Peak to the next peak

Visible Light = between 400nm and 750nm

Amplitude - Amp or A units – m, meters, “Height” of the wave

Frequency – ƒ units- Hertz, Hz or 1/s, Amount of waves passing a spot every second

1 megahertz = 1 million Hz = 1 x 106 Hz

The EM spectrum:

R-M-I-V-U-X-G: All travel at speed of light

Energy = Planck’s constant times Frequency Calculate energy given frequency

E = hf h = Planck’s constant = 6.626x10-34 J sGiven f = 1.25 x1017 1/s Find E E = (6.626x10-34 J s) x (1.25 x1017 1/s) = 8.28 x 10-16 J

Given E find f E = 6.626 x 10 -12 J

Notes-Temp in the Universe

o Temperature

o Wien’s lawo Stephen Boltzmann Law, Planck’s law

Temperature

Motion represents a form of energy known as thermal energy, heat. Temperature is a direct measure of this internal motion

Fahrenheit temperature scale

Celsius scale: freezes at 0 degrees (0° C) and boils at 100 degrees (100° C)

Although we know of no matter anywhere in the universe that is actually this cold, temperatures can in theory reach as low as -273.15° C. This is the temperature at which atomic and molecular motion all but ceases. It is convenient to construct a temperature scale based on this lowest possible temperature, or absolute zero.

Scientists commonly use such a scale, called the Kelvin scale in honor of the nineteenth-century British physicist Lord Kelvin. Since it takes absolute zero as its starting point, the Kelvin scale differs from the Celsius scale by 273.15°.

Kelvin = celsius degrees + 273

Translational motion ceases at 0 kelvins (0 K). Water freezes at 273 kelvins (273 K). Water boils at 373 kelvins (373 K).

Examples of Converting from Kelvin to Celsius and vice versa from board

•

Radiation Laws

Wien’s Law, Stefan-Boltzmann Law, and Planck’s Law, kichoff’s law • Blackbodies – Perfect emitters of radiation – Emit the maximum possible radiation at every wavelength – and perfect absorbers – Absorb all incident radiation. • Blackbodies are hypothetical, ideal radiators• Everything else is considered a grey body• However, the Sun is nearly a blackbody

Wien’s Law• Tells us that hotter objects radiate energy

at shorter wavelengths.• Peak solar radiation intensity has a wavelength of 0.5 μm (micrometers)• Peak Earth radiation intensity has a wavelength of 10 μm• For any radiating body, the wavelength of peak emission is given by Wiens Law.• Short wave radiation < 0.4 μm • Longwave radiation > 0.4 μm

Wien’s Displacement Law:Λmax = 2897 /T• λ max =wavelength of maximum radiation emission (μm)• Τ = temperature of the emitting surface (K)• 2897 = Constant

Example 1:What is the wavelength of maximum radiation for a blackbody at a temperature of 25°C?

λmax =2897 / T λmax =2897/(25 + 273.15) = 9.72 μm

Invert the equation to solve for temperature

What is the temperature of a surface whoswavelength of maximum radiation is 1 μm? 15 μm?λmax =2897/ T → T = 2897 / λmax

T = 2897/ 1 = 2897 K = 2624 °CT =2897/ 15 = 193 K = - 80 °C

Stefan-Boltzmann Law• The single factor that determines how much energy a blackbody radiates is its temperature• Hotter bodies emit more energy than do cooler ones• The intensity of energy radiated by a blackbody increases according to the fourth power of its absolute temperature.I = σT 4I = intensity ofradiation in W m‐2σ = Stefan‐Boltzmann constant(5.67 X 10‐8 W m‐2 K ‐4 )T = isthe temperature ofthe body in Kelvin

Example 1:

• How much radiation is emitted by a blackbody at a temperature of 25ºCFirst step: Convert Celsius to Kelvin T (K) = 25 (ºC) + 273.15 = 298.15 KSecond Step: Plug values into equation I = σT4

I = 5.67 x 10-8 x 298.154

I = 448 W m-2

Grey Bodies

• True black bodies do not exist in nature• Most liquids and solids must be treated as grey bodies which means they emit some percentage of the maximum amount of radiation possible at a given temperature.• The percentage of energy radiated by a substance relative to that of a blackbody is referred to as its emissivity (ε).

By incorporating the emissivity of any body, we derive the general version of the Stefan-Boltzman Law: I = εσT4

Example 2: • For a greybody at the same temperature (25°C), what is the radiation emitted if the emissivity is 0.7?• I = 0.7 x 5.67 x 10-8 x 298.154

• I = 0.7 x 448• I = 314 W m-2

If we know the intensity, we can then solve for temperature

Example 3:• What is the temperature (°C) of a blackbody that is emitting 1000 W m-2?• Rearranging I = σT4

we get:• T = (I/σ)0.25

• T = (1000/ 5.67 x 10-8)0.25

• = 364.42 K • = 91.27 °C

Warm-up 10/1

SB constant: 5.67 x 10-8Wm-2K-4 Wien’s Law constant: 28971. How much energy is emitted by a surface whose temperature is 230 K?

158.67 Wm-2

2. If an object has a temperature of -180 degrees C, how much energy per square meter does it emit?4.24 Wm-2

3. What is the temperature of a surface that emits 0.0000000043 W per square meter?0.525 K

Wrap -up 10/1

1. 5.0 x 10 -9 W per square meter strikes a field of grass with an average albedo of 0.6. How much energy is reflected? How much is absorbed?3 x 10-9 reflected; 2 x 10-9 absorbed

Turned in as classwork Notes IDRDP

I n t e r f e r e n c eC o n s t r u c ti v e - a d d i n g w a v e s m a k e s a m p l i t u d e l a r g e rD e s t r u c ti v e - a d d i n g w a v e s m a k e s a m p l i t u d e s m a l l e r

D i ff r a c ti o n - b e n d i n g o f l i g h t a r o u n d a g r a v i t a ti o n a l o b j e c t

R e f r a c ti o n - b e n d i n g o f l i g h t t h r o u g h m a t e r i a l

R e fl e c ti o n - M i r r o r i m a g e o f a n o b j e c t

D o p p l e r E ff e c t - L o n g w a v e l e n g t h , l o w e r f r e q u e n c y , a w a y o b s e r v e r - r e d s h i ft- s h o r t e r w a v e l n g t h h i g h e r f r e q u e n c y , t o w a r d o b s e r v e r -b l u e s h i ft

P o l a r i z a ti o n - t h e o r i e n t a ti o n o f t h e o s c i l l a ti o n i n a w a v e i s p e r p e n d i c u l a r t o m o ti o n ( r o l l e r c o a s t e r )

Critical thinking

Describe the structure of an atom.

Waves & Electromagnetic Spectrum Worksheet

Directions: Use the word bank to answer the following questions. Each word will be used only once.

1. ____________________ waves are used to penetrate solids and are used in doctor’s offices and as airports.

2. ____________________ is the distance between one point of a wave to the same point in the next wave.

3. ____________________ is the number of waves per unit of time.

4. ____________________ waves occur when the motion of the medium is parallel to the direction of the wave.

5. ____________________ waves have a color spectrum known as ROYGBIV.

6. ____________________ waves disturb matter.

7. The ________________ is the top of a wave.

8. The ________________ is the bottom of a wave.

9. ____________________ is the maximum distance that matter is displaced from the resting position.

10. ___________________ waves are produced by stars and galaxies.

11. ___________________ waves occur when the motion of the medium is at right angles (perpendicular) to the direction of the wave.

12. ___________________ waves are often used in heat lamps.

13. ___________________ waves are utilized by insects to locate nectar.

14. ___________________ waves are transverse waves that disturb electromagnetic fields.

15. ___________________ waves have the shortest wavelength and the highest frequency.

Crest Frequency Mechanical InfraredTrough Transverse Radio GammaWavelength Longitudinal Ultraviolet X-RaysVisible Light Amplitude Electromagnetic

Wrap-up

1. Calculate the wavelength of the electromagnetic radiation whose frequency is 7.5 x 1012 Hz.

2. Determine the frequency of light with a wavelength of 4.2 x 10-9 m. (Watch your units!)

3. Determine the energy (in joules) of a photon whose frequency is 3.55 x 1017 Hz.

4. What is the frequency of a radio wave with energy of 1.55 x 10-24 J/photon?

6. Cobalt-60 is an artificial radioisotope that is produced in a nuclear reactor for use as a gamma-ray source in the treatment of certain types of cancer. If the wavelength of the gamma radiation from a cobalt-60 source is 1.00 x 10-3 nm, determine its energy in joules/photon.