Lecture 11Lecture 11Matter and LightMatter and Light

Astro161 – Fall 2011Dr. Matthias Dietrich

Homework

The second home-work assignment is available after class today and it is also posted on the class web-site, as well as on Carmen. It will be due on Monday, Oct. 24th .

The home work has to be returned either in class

or as e-mail:

dietrich@astronomy.ohio-state.edu

antognini@astronomy.ohio-state.edu

some announcement

This Friday, October 21st, will be the second midterm.On Thursday, Oct. 20th, there will be a review session in the planetarium onthe 5th floor of Smith Lab at 5pm.

A practice test is posted, again on the class web-site and also on Carmen.

Oct. 03 Mon. doneOct. 04 Tue. doneOct. 05 Wed. doneOct. 11 Tue. doneOct. 12 Wed. doneOct. 13 Thu. doneOct. 17 Mon. @ 6:00 pmOct. 18 Tue. @ 6:00 pm

Smith Lab. 5th floor Planetarium

Roof NightsOct. 06 Thu. 8:00 pm doneOct. 19 Wed. 8:00 pm (Oct. 26)

Lecture 11Lecture 11Matter and LightMatter and Light

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In the late 17th and early 18th century experiments with prisms and slits – dispersion and diffraction – lead to thepicture that light can be described as a wave phenomenon.

Particle ? Wave ?Wave

Lecture 2: Light

Properties of Waves

• Light waves are characterized • by three numbers:

– wavelength, λ (size of the wave)

– frequency, f (number of waves/second)

– wave speed, c (the same for all wavelengths)• These are all related by:

c = λ f

• longer wavelength means smaller frequency

wavelength

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Wavelength (Å)

5000 10000 15000 200000

T = 6000 K

T = 10000 K

Hotter blackbodies:• emit more energy at all wavelengths• peak at shorter wavelengths

The Black Body Radiation Curve

Wien’s Law Stefan - Boltzmann

Lecture 2: Light

The Doppler Effect

• Shift in the observed wavelength when the source is moving relative to the observer.

• Examples:– Sound Waves (Siren or Train Horn)– Light Waves

• Amount of the shift and its sign depends on• relative speed of the source and observer• direction (towards or away)

Lecture 2: Light

The Doppler Effect for Light

• Amount of the shift depends upon the emitted wavelength (λem) and the relative speed v:

• If the motion is away from observer

• Wavelength gets longer = REDSHIFT

• If the motion is towards the observer• Wavelength gets shorter = BLUESHIFT

Way to Measure Speeds• Observe the wavelength (obs) of a source with a known

emitted wavelength (em)

• The difference is directly proportional to

the speed of the source, v:

(For v very small compared to the velocity c of light)

rest frame

observed

5050Å – 5007Å 5007Å= 0.0086 · cv = 2575 km/s

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Doppler Effect in Practice

• Used by astronomers to measure the speeds of objects towards or away from the Earth.

• Other Uses:• Traffic Radar Guns:

– Bounce microwaves or laser light of known wavelength off of cars, measure reflected wavelength: Doppler shift gives the car’s speed.

• Doppler Weather Radar:– Bounce microwaves off of clouds, measure speed and

direction of motion. Strength of the reflected signal gives the amount of rain or snow.

Lecture 2: Light

Doppler Effect and the Shifts of Wavelength

– shift to the red if the object is moving away– shift to the blue if the object is moving closer– a way to measure speeds at a distance e.g. how fast a star or galaxy moves away or how fast a car is moving

Analysis of Light

• Energy which is emitted• Temperature of a body, e.g. a star• Motion of an object along the line of sight

First Ideas

• Greek philosophers

e.g. Democritus (~460 – ~370 BC)

‘Matter consists of tiny particles (Greek atomos)

which cannot be further divided and they have

already the properties of the matter they build.’

What is Matter ?

Ernest Rutherford (1910):Experiments to get an idea about the internal structure of atoms.

Most of the mass is concentrated in a compact nucleus smaller than 10-15 m and containing at least 99.98% of the mass which is surrounded by negatively charged electrons.

radioactivematerial

α-particles

Rutherford’s Model of an Atom

not in scale!

This only a simple model to providea sort of picture of an atom.

Just to illustrate the size and emptiness of an atom imagine:

the size of the Sun is scaled down to the size of the nucleus of an atom (~10-15 m).

The electrons would move around the nucleus (~10-10 m) in a distance which would correspond to ~25x the distance of Pluto to the Sun.

But remember, this is only a picturewhich tries to visualize an atom.

WRONG

Electrons don’t orbit around the nucleus like planets around the Sun.

Electrons, protons, and neutrons are not little particlesbut they have particle and wave properties like light.

How do we know all this?

Particle acceleratorfor example CERNnear Geneva.

~9 km

Underground there are labs with huge detectors whichrecord the decay of particles which are created whenfor example protons or electrons collide head-on.

Whereas the gravitational force is always attractive, the electromagnetic force can be attractive or repulsive because charges come in two types (positive and negative):

– opposite charges attract

– like charges repel

✚

✚

✚

Atomic Structure

• Atomic Structure– Atoms are formed by the electromagnetic force

- +r

221

r

qqF

q1 q2

Coulomb Law

Atomic Structure

• The atomic nucleus (size ~10–15 m) consists of two types of particles of nearly equal mass:– Protons (positive electric charge)

– Neutrons (no electric charge)

+

Atomic Structure

• The atomic nucleus (size ~10 –15 m) consists of two types of particles of nearly equal mass:– Protons (positive electric charge)– Neutrons (no electric charge)

• The atomic nucleus is held together by the strong nuclear force, the strongest force in nature, but with a very short range.

Atomic Structure

The Strong Nuclear Force

0

F

r

Electromagnetic repulsion

Strong nuclear attraction,a very short-range force

Principal Subatomic Particles

Name Size Mass Charge

Electron (e–)

Point? 9.1 × 10–31 kg (= 1 me)

–1

Proton (p+)

10–15 m 1836 me +1

Neutron (n)

10–15 m 1838 me 0

Photon -------- 0 0

-+

Important Atomic Nuclei

• Hydrogen (H)– 1p, 0n– Weight = 1

+

• Hydrogen (H)– 1p, 0n– Weight = 1

• Deuterium (D)– 1p, 1n– “heavy hydrogen”– Weight = 2

+

+

the isotope of hydrogen

Important Atomic Nuclei

• Helium (He)– 2p, 2n– Weight = 4

+

+

Important Atomic Nuclei

• Carbon (C12)– 6p, 6n (common)– Weight = 12

+

+ +

+

+

+Other isotopes havedifferent numbers ofneutrons C13 (7n) C14 (8n)

Important Atomic Nuclei

latest count – 116 elements

Atoms

+

+- -

Massive nucleus held together by strongnuclear force. Electrons “orbit”, held by electro-magnetic force.

number of electrons equals

number of protons

nucleus

cloud ofelectrons

Ions

+

+-

Ions are “charged”Atoms, i.e.number of e- number of p+

Here two protons and only one electron

positively charged ion

Molecules

Molecules are collections of atoms that “share” electrons. Molecules are held together weakly by the electromagnetic force.

H2

Hydrogen

Helium

Oxygen

Neon

Iron

Atomic Structure

• Electrons are allowed only in

certain orbits which have

specific energies.

• Electrons can change orbits by gaining or losing fixed amounts of energy.

• This can be done by absorbing or emitting a photon of the correct energy.

Niels Bohr (1885 – 1962) postulated:

The Atomic Model by Niels Bohr

Electrons are allowed only on discrete orbits with specific energies.Transitions between the orbits require discrete excitation energies.

Balmer discovered thatfor hydrogen the wavelengths for specific transitions are given by

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Emission/De-excitation An electron drops to a lower-energy orbit, emitting a photon.

Before After

photon

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Absorption/Excitation A photon is absorbed, the electron goes to an excited state.

AfterBefore

photon

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Absorption/Re-Emission Sequence

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PhotoionizationA high-energy photon can remove an electron from an atom.

AfterBefore

highenergyphoton

Cooling by Collisions• Since photons can carry away energy,

photon emission can cool a hot gas.– Temperature is a measure of average speed

of particles in the gas.

Hot GasFaster Average Speeds

Cool GasSlow Average Speeds

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Step 1: Two high-speed atoms

collide.

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Step 1: Two high-speed atoms

collide.

Step 2: Some ofcollision energy is

used to excite electrons.

Exchange of kinetic for

internal energy.

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Step 1: Two high-speed atoms

collide.

Step 2: Some ofcollision energy is

used to excite electrons.

Exchange of kinetic for

internal energy.

Step 3: Atomsde-excite, losing

energy to photons,which escape.

• The net result of the collision is that the particles are moving slower (so average speed of gas particles and temperature decreases) and photons carry away energy.

• Energy is conserved, but converted from one form (gas kinetic energy) to another (photons).

Cooling by Collisions

Atomic Structure

• Energy levels (allowed orbits) are different for each ion. Depends on the following:– Primarily on number of electrons– Secondarily on number of protons– To a small extent on the number of neutrons

• Each element has a unique signature

(like a fingerprint)

Model Hydrogen Atom

UV

Visible

Infrared

Atomic Line Spectra

Hydrogen

Helium

Sodium

Mercury

If atoms are densely crowded, energy levels

are perturbed by neighboring charges

• If atoms are densely crowded, energy levels are perturbed by neighboring charges random shifts of energy levels random shifts of photon energies broadening of spectral lines

Atomic Structure

Low Pressure

Medium Pressure

High Pressure

Solid, Liquid, or Dense Gas

• If atoms are densely crowded, energy levels are perturbed by neighboring charges random shifts of energy levels random shifts of photon energies broadening of spectral lines

• Solids, liquids, and very dense gases emit continuous spectra

Atomic Structure

What can we learn from analyzing light ?

• Temperature (Kelvin Scale)– measures internal energy content.

• The size of an object (L = 4πR2 σT4)

• Kirchoff’s Rules of Spectroscopy

Kirchhoff’s Rules

Kirchhoff’s rules are a set of empirical guidelines that tell us what happens when light andmatter interact.

1 a hot dense object produces a

continuous spectrum

2 a cool diffuse gas in front of a hot source produces an absorption spectrum

3 a diffuse gas seen against a dark back-ground produces an emission-line spectrum

HotContinuum

Source

Continuous Spectrum Emission-Line Spectrum

Absorption Spectrum

Cool, DiffuseGas Cloud

Absorption-Line Spectrum

• Light from a continuous spectrum through a vessel containing a cooler gas shows:– A continuous spectrum from the lamp crossed

by dark “absorption lines” at particular wavelengths.

– The wavelengths of the absorption lines exactly correspond to the wavelengths of emission lines seen when the gas is hot!

– Light is being absorbed by the atoms in the gas.

Emission-Line Spectra

• 19th century: Chemists noticed that each element, heated into an incandescent gas in a flame, emitted unique emission lines.

• (Fraunhofer, Bunsen, Kirchoff)– Mapped out the emission-line spectra of

known atoms and molecules.– Used this as a tool to identify the

composition of unknown compounds.– They did not, however, understand how it

worked.

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TelescopesTelescopes