Chapter 5 Light and Matter

Chapter 5 Light and Matter

Stars and galaxies are too far for us to send a spacecraft or to visit (in our lifetimes). All we can receive from them is light But there is much we can learn (composition, temperature, speeds, etc.) by studying the LIGHT they emit! Radio Light Visible Light X-ray Light

An example are the following images of the galaxy NGC-5128 (Radio source Centaurus A) obtained at different wavelengths Radio Light Centaurus A Visible Light

Centaurus A Infrared Light Visible Light

What is light? Newton suggested that light is made of countless tiny particles. Other scientist conducted experiments that suggested that light behave like a wave. This problem is still not solved: Is light a wave or a particle? This different behavior of light is called the wave-particle duality of light. For some experiments, it is better to treat light as a wave, for others, it is better to treat light as a particle. Light behave as an electromagnetic wave (electric and magnetic fields oscillating) Light can behave like a particle. These particles are called photons

Let s take a look to the behavior of light as a wave A simple example are waves created by throwing a rock in a pond The water doesn t move in the direction away from the point were the rock created the waves Information is carried from place to place without physical movement of material

Wave characteristics: How do we describe a wave? Parameters that describe a wave: Wavelength, amplitude, frequency, wave speed

Wavelength (Unit of length: cm, nm, ) Distance between successive wave peaks Period (Units of time: s) Time between passing of wave crests Frequency (Unit: Hertz, Hz = 1/s) Number of vibrations per unit time Wave Speed (Units of velocity: m/s, km/s) Wave Speed = Wavelength x Frequency In the case of light : C = wavelength x frequency C = λ x f λ = wavelength (lambda) f = frequency Important: Light at all wavelengths travels in vacuum at the same speed: c = 300,000 km/s

Relationship between frequency and wavelenghth for different frequencies Low frequency means longer wavelength Higher frequencies means shorter wavelength

Electrically charged particles and electromagnetic waves Electrons have charge Protons have + charge Both have electric fields + attract, ++ and repel The changing position of a charged particle creates waves called electromagnetic waves The electromagnetic waves travels through empty space (Vacuum). Visible light is an electromagnetic wave

Effect on electrons by a passing electromagnetic wave

Magnetism Moving electric charges also produce Magnetic fields. Example: electric motors Another example: The Earth s magnetic field is produced by the spinning of charges in the liquid metal core of the Earth. Conversely, magnetic fields force charged particles to move.

Accelerated charges (electrons, protons) produce: Ripples in the ElectroMagnetic (E&M) field = E&M Waves = LIGHT! An electromagnetic wave is composed of two oscillating fields, an electric field and a magnetic field perpendicular to each other

Newton experimented with light. He sent white light through a prism and was able to obtain all the colors of the rainbow. This was something known already Was it the prism that added something that produced the colors? If one of the colors is sent through the prism, it does not produce all the colors. Colors are intrinsic to white light One can split light onto colors using a prism or a diffraction grating. A diffraction grating is composed of many parallel lines ( example 1000 lines/mm) A prism split light by refraction (dispersion) A diffraction grating split light by diffraction (interference)

Wavelength means COLOR 400nm 500nm 600nm 700nm Visible light ranges in wavelength from ~400 to ~700 nanometers.

Electromagnetic Spectrum Microwaves, cooking communication heat detected by our eyes sunburn penetrate tissue most energetic

Visible light is a small part of the EM spectrum.

Did you ever wonder why astronomers put telescopes on mountaintops?

The temperature scale Comparison of Kelvin, Celsius and Fahrenheit scales The scale used in astronomy is Kelvin. The unit is Kelvin (K)

Blackbody Radiation The atoms and molecules that make up matter are in constant motion. The temperature of an object measures the amount of motion of the particles. The higher the temperature, the faster the particles move. When the charged particles change their state of motion, electromagnetic radiation is emitted.

Stellar Colors Reddish coolest stars (~3000 K) Orange-ish Yellowish White Sun (~6000 K) Bluish hottest stars (~50,000 K) Stars, light bulbs, irons, etc., are ~Blackbodies with different colors, depending on their temperature. A Blackbody is a perfect emitter and absorber, whose temperature defines how much light it emits at each wavelength.

Blackbodies, like stars, light bulbs and irons, emit this characteristic spectrum of light: Blackbody Spectrum:

Blackbodies with different temperatures look like this: Hotter blackbodies are brighter and bluer. (nm : nanometer 1 nm = 10 ⁹ m)

Wien s Law Hotter bodies radiate more strongly at shorter wavelengths (i.e. they re bluer). Cooler bodies radiates more at longer wavelengths (i.e. they are redder) There is a wavelength at which the radiation reaches a maximum ( max ) max = 2,900,000 T (K) nm If we know or we can find max from the radiation curve, using Wien s law equation we can measure a star s temperature from its spectrum! Or if we know the temperature T, we can find the max Example: For the Sun, T= 5800 K, max =500 nm

Stefan s Law Hotter blackbodies are brighter overall (at every wavelength). F = T 4 where: F = total radiative flux = constant T = Temperature of black body in K The total radiated flux or total energy radiated per second is proportional to the fourth power of T. It is equivalent to the area under the black body curve

(Flu x)

Comparison of blackbody curves from four astronomical objects at different temperatures 1 nm = 10 ⁹ m

Spectroscopy (Analysis of Spectra)

Continuous Spectrum

Emission Line Spectrum

Emission Line Spectra Each element produces its own unique pattern of lines The set of emission or absorption lines is unique for a chemical element. They are the fingerprint of an element

Absorption Line Spectrum

Absorption Line Spectra Spectrum of the Sun The H letter (Hydrogen) followed by a Greek letter are used for the Balmer series. The Balmer series of H is the series of lines emitted in the visible part of the spectrum

Three Types of Spectra Continuous Emission Lines Absorption Lines

Kirchhoff s First Law Published in 1859 Hot, dense gases or solids produce a continuous spectrum. Example: Light bulb filament Continuous Spectrum

Kirchhoff s Second Law A hot, rarefied gases when exited (By an electric current or UV emission) produce an emission line spectrum. Examples: Neon signs, Sodium vapor street lamps, emission nebulae Emission Line Spectrum

Kirchhoff s Third Law A cool gas in front of a hot continuous source produces an absorption line spectrum. Example: The Sun, stars Absorption Spectrum

Summary of Kirchoff s Laws: 1 2 3 How can we explain the discrete emission or absorption in lines?

The Nature of Atoms Three subatomic particles makeup an atom: 1. Proton - positive charge 2. Neutron - no charge 3. Electron - negative charge Like charges repel so a large amount of force is required to keep the protons in the nucleus together. mass of proton mass of neutron 1836 x mass of electron Atoms are mostly empty space! And, since all matter is made up of atoms, matter is mostly empty space!! If an atom loses or gains an electron, it is said to be ionized and it is therefore an ion. It has a positive charge if it looses electrons or negative if it gain electrons Atoms can bond with other atoms of the same kind or different kind to form molecules.

Each atom of a given element contains a specific number of protons and electrons thus making that element unique.

Bohr s Hydrogen Model Niels Bohr e - Electron orbits the proton (i.e. nucleus) kept in place by the Coulomb Force (F c ). 1 F c R 2 p + How does this structure lead to unique emission and absorption lines?

Electrons can only be in particular orbits (energy states). Energy is quantized (Quantum Mechanics). Bohr Model Excited state (higher energy) Ground state (lowest energy) Excitation requires energy to be added to the atom De-excitation - energy is released from the atom e p

electrons gain energy nucleus R 2 R 3 E 2 E 3 R 1 R 2 R 1 E 1 lose energy R3 E = E 3 -E 1 Electron needs to gain energy to move from R 1 to R 3 (excited). Electron needs to lose energy to move from R 3 to R 1 (de-excited). How does the electron get the energy it needs to become excited? 1. Collisions between atoms can excite electrons to higher energy levels. Passing an electric current (High voltage in a gas)will make atoms collide. 2. The absorption of energy from light can excite electrons.

What s going on? Light can behave as a particle. Light energy must be carried in packets called photons. Albert Einstein Einstein was awarded the Nobel Prize in 1921 for his theory of the photoelectric effect. The effect can be explained if light is considered as a particle (photons) Light Energy 1/wavelength Light Intensity = # photons arriving/second Low energy photons cannot cause e ejections. High energy photons cause ejection

Quantum Mechanics: Atoms can only absorb or emit photons with energies exactly equal to the energy difference between electron orbits. The energy of a photon is related to the wavelength or the frequency f: E ph 1/ f E ph = h f = h c/ (f = c/ ) h is the Planck s constant Larger orbital jumps have larger energy levels and radiates shorter wavelength (or higher frequency) photons

The energy of the photon must be precisely equal to E. E p E E p = E Photon absorbed photon emitted E p = E

Atoms of different elements have unique energy level structures. The figure on the left, shows some of the energy levels of Hydrogen. Every e transition corresponds to a unique wavelength. Ionization = ejection of e. An ionized atom has a different set of lines, different from the neutral atom. Lyman (UV) Balmer (Visible) Paschen (IR) The figure at the bottom shows the Balmer series of Hydrogen. Part of the lines of this series are in the visible part of the spectrum. Hydrogen

Examples of spectra of different elements. Every element (atom) emit a unique set of lines. It is the fingerprint of that particular atom.

Bohr s Hydrogen Atom In modern quantum mechanics: Electrons are not just particles, but also waves, without exact locations.

The Doppler Effect In moving sources, like fire trucks and race cars, there is change pitch of the sound of a siren as they go by. The pitch is higher when they are approaching and lower when they are moving away. This is an example of Doppler effect in sound waves

Doppler effect Motion along the line of sight (radial motion) produces a Doppler effect No Doppler effect if the motion is perpendicular to the line of sight

Doppler effect in electromagnetic waves Electromagnetic waves also present the Doppler effect. Light emitted by a moving object present Doppler effect The equation of the Doppler effect related the radial speed of the object with the change in wavelength v/c = Δ / = ( shift - rest)/ rest v is the radial velocity of an object c is the speed of light Δ is the change in wavelength (shifted - rest ) is the rest wavelength

The Doppler Shift Stationary source: Moving source:

The Doppler Shift If the object is receding (moving away from observer), it will show Doppler red shifted lines (lines shifted toward the red) If the object is approaching the observer (moving toward the observer) it will show Doppler blue shifted lines (lines shifted toward the blue) The example below show the Hydrogen Balmer series lines red shifted, at rest, and blue shifted

Obtaining the rotation of an object from the width of the Doppler lines If an object (a planet, a star or a galaxy) is rotating, the side approaching the observer will be blue shifted. The side moving away form the observer will be red shifted. The line emitted from the center will have no shift. As a consequence, the line will be wider that it would if the object had no rotation. The rotation rate of the object can be determined by measuring the width of the spectral lines

What can we learn from spectroscopy? The chemical composition by comparing spectral lines with laboratory spectra of atoms. The temperature by matching overall spectral shape with blackbody curve or by using the Wien s law equation. The line-of-sight velocity by determining Doppler shift. The rotation rate by measuring broadening of spectral line due to Doppler shift. The pressure of the gas in the emitting region due to broadening of spectral lines. The greater the pressure, the broader the line