## LECTURE 11: Atoms and Light

Key Questions:
• What are atoms, what are they made of, and what holds them together?
• What is the relation between atoms and chemical elements?
• What are electromagnetic waves? How are they related to visible light?
• What are the various forms of electromagnetic radiation?
• What speed does electromagnetic radiation travel at?
• What are photons? How is the energy of a photon related to its wavelength?
• What can the spectrum of EM radiation from an object tell us about its
• surface temperature?
• chemical composition?

### ATOMS

All material objects are made of atoms, which are themselves made up of protons, neutrons, and electrons.

• Ancient Greek idea, proposed by philosopher Democritus.
• First modern evidence from chemistry, in mid 19th century,
• Basic unit of most substances is the molecule.
• All molecules made from a finite set of (about 110) chemical elements.
• A molecule consists of two or more atoms held by electrical forces.
• Understanding structure of atoms is a (perhaps the) major achievement of 20th century physics.

### CONSTITUENTS OF ATOMS

Atoms are made of protons (p), neutrons (n), and electrons (e).

• Protons and neutrons form nucleus of atom.
• Electrons "orbit" nucleus. Diameter of orbit roughly 104 x diameter of nucleus.
• Proton has positive electric charge.
• Neutron has (almost) same mass as proton, but no electric charge.
• Electron has 1/2000 mass of proton, negative electric charge.

### THE FOUR FORCES

There are only four basic forces in nature: gravity, electromagnetic, and the strong and weak nuclear forces.

• Electromagnetic: opposite charges attract, like charges repel. Holds electron to nucleus.
• Strong nuclear: holds protons and neutrons together in nucleus.
• Weak nuclear: weaker effects within atoms, causes some radioactive decays.
• Gravity: much weaker than others, but affects everything, and always attracts. Wins on large scales.

### CHEMICAL ELEMENTS

The number of protons in an atom determines its chemical behavior.

• Under usual terrestrial conditions, an atom has the same number of protons and electrons.
• Chemical bonds (which hold molecules together) are formed by electrons.
• Chemical properties of atom depend on number of electrons, hence number of protons.
• Number of neutrons usually similar to number of protons.
• Examples:
• 1 proton, no neutrons: hydrogen
• 2 protons, 2 neutrons: helium
• 6 protons, 6 neutrons: carbon
• 8 protons, 8 neutrons: oxygen
• 26 protons, 30 neutrons: iron.

### THE SPEED OF LIGHT

In empty space, light travels at a constant, finite speed,

c = 300,000 km/s = 3 x 108 m/s.
• First measured by timing eclipses of Jupiter's moons, which appear delayed when Jupiter is further away.
• Speed of light is fast, but not infinite.
• We see distant objects as they were in the past.
• Earth-Sun distance is eight light-minutes.

### ENERGY

• Roughly speaking, energy is ability to do something.''
• Physics allows precise definition.
• Energy comes in different forms, e.g., kinetic (energy of motion), thermal (energy of hot stuff), electrical.
• Also potential energy, available to be tapped, e.g., gravitational or chemical.
• Energy can be transformed, but total energy always conserved.
Examples:
• Electric heater converts electrical energy to thermal energy.
• Hydroelectric dam converts gravitational potential energy to electrical energy.
• Photosynthesizing plant converts energy of light from Sun to chemical potential energy.
• Coal burning plant converts chemical potential energy to electrical energy.

### WAVES

• A wave is a propagating, periodic disturbance.
• Examples: ocean wave, sound wave, stadium wave.
• Waves don't move stuff from place to place.
• But they can transmit energy.
• Waves can interfere'' with each other, adding together or canceling.
Characteristics of waves:
• Characterized by wavelength, frequency, speed.
• Denoted \lambda, \nu, cwave.
• \lambda = distance between successive peaks (or troughs).
• \nu = number of peaks per second.
• Therefore cwave = \lambda x \nu.
• Another characteristic: amplitude, e.g., height of ocean wave.
• For sound waves: frequency determines pitch, amplitude determines volume.
• Speed of sound in room temperature air, 300 m/sec.

### ELECTROMAGNETIC WAVES

• Electric fields: exert force on charged particles.
• Magnetic fields: exert force on magnetized objects.
• Changing electric fields produce magnetic fields.
• Changing magnetic fields produce electric fields.
• Unified theory of electromagnetism (Maxwell, 1860s), predicts existence of propagating electromagnetic waves:
• Produce changing electric field by accelerating charged particles.
• Causes changing magnetic field nearby.
• Causes changing electric field further along. Etc.
• All such waves propagate at same speed, regardless of frequency.
• Predicted speed matches measured speed of light.

### VISIBLE LIGHT

Visible light is a form of electromagnetic wave. The wavelength of light determines its color.

• From long wavelength to short: Red, Orange, Yellow, Green, Blue, Indigo, Violet.
• R O Y G. B I V.
• Convenient unit: 1 nano-meter (nm) = 10-9 meter.
• Red light: 700 nm.
• Violet light: 400 nm.
• Frequencies: 4.3 x 1014 to 7.5 x 1014 waves/sec.
• A prism bends light because speed in glass less than speed in vacuum (or in air). Called refraction.''
• Bends blue light more than red because glass slows blue light more.
• White'' light is really a superposition of colors, which can be separated with a prism.

### THE ELECTROMAGNETIC SPECTRUM

There are other forms of electromagnetic radiation. All of them travel (in empty space) at the speed of light c.

From long wavelength (low frequency) to short wavelength (high frequency):

• Radio and microwave (greater than ~ 1 mm = 106 nm)
• Infrared (~ 106 nm - 103 nm)
• Visible: R O Y G B I V (~ 700 - 400 nm)
• Ultraviolet (~ 100 - 10 nm )
• X-rays (~ 10 - 0.01 nm)
• Gamma rays (less than ~ 0.01 nm)

Earth's atmosphere is opaque to many forms of electromagnetic radiation.
Windows of transparency: visible and part of radio.

### PHOTONS

EM radiation travels in discrete packets of energy, called photons, which can be thought of as particles of light.''

The energy of a photon depends on its wavelength; shorter wavelength = higher energy.

• EM radiation has many wavelike properties --- refraction, interference.
• In early 20th century, Planck and Einstein showed that it travels in discrete packets of energy, known as photons.
• Counter-intuitive for something to be both particle and wave, but that's the way nature is.
The energy of a photon is
E = h c / \lambda
E = energy of photon
\lambda = wavelength of photon
c = speed of light
h = Planck's constant (a universal number).

• Short wavelength photons have more energy.
• Radio photon: not much energy.
• Gamma-ray photon: lots of energy.
• Energy emitted by an object = (number of photons emitted) x (average energy per photon)
• To affect an atom or molecule, photon requires minimum amount of energy.
• Example: UV, X-ray, Gamma-ray photons affect DNA molecules, cause cancer. Radio photons, even at much higher intensity, do not.

For many purposes in astronomy, more useful to think of light (and EM radiation) in terms of photons rather than waves.

### TEMPERATURE AND DEGREES KELVIN

• Common temperature scales: Farenheit (F), Centigrade (C, a.k.a. Celsius).
• Temperature measures how fast atoms are moving.
• If atoms are completely still, temperature is absolute zero.
• Standard temperature scale in physics is Kelvin Degrees (K).
• Absolute zero: 0 K, -273 C, -473 F.
• Freezing point of water: 273 K, 0 C, 32 F.
• Boiling point of water: 373 K, 100 C, 212 F.
• Room temperature: 293 K, 20 C, 68 F.

Opaque objects emit EM radiation with a characteristic, continuous distribution of wavelengths called a blackbody spectrum.

The wavelength of peak emission depends on the object's temperature: hotter objects emit more energy at shorter wavelengths.

Consider a body that could absorb all light that falls on it.

• No reflection, thus black'' body.
• If the temperature of the body is above 0 K, it glows, emitting EM radiation.
• If it is warmer than its surroundings, it emits more energy than it absorbs.
• Luminosity (rate of emitting energy) is proportional to (surface area) x T4.
• Characteristic distribution of wavelengths is called a blackbody spectrum.
• Peak emission wavelength is shorter for hotter bodies:
\lambdamax = 500 nm x (6000 K / T)
Examples:
• Surface of sun, 6000 K, peak emission at 500 nm, yellow light.
• For 12000 K, peak at 250 nm, ultraviolet light.
• For 3000 K, peak at 1000 nm, infrared light.
• For 300 K, room temperature, peak at 10,000 nm, also infrared.
• Room temperature bodies glow at wavelengths around 10,000 nm; warmer bodies glow more brightly.
• Night scopes'' detect this radiation, convert it to visible light.

### ATOMIC FINGERPRINTS IN SPECTRA

The spectrum of an object is the distribution of its emitted electromagnetic radiation.
We often show the spectrum with a plot of emitted energy vs. wavelength.

Atoms like to emit and absorb light at particular wavelengths, producing spectra with discrete lines.
Each type of atom has a characteristic spectral fingerprint.''

Absorption and emission lines:

• Electons in atom can only move in orbits with specific, discrete energies.
• Atoms absorb photons with energies that can move electrons from one orbit to another.
• This absorption can remove photons of specific wavelengths from a continuous spectrum, producing dark absorption lines.
• When an electron drops from one orbit to another, the atom emits a photon with the liberated energy.
• A gas of energetic atoms can produce bright emission lines.
• Wavelengths of emission and absorption lines depend on energies of electron orbits, which are specific to each type of atom.

### WHAT CAN WE LEARN FROM AN OBJECT'S LIGHT?

Spectra of astronomical objects (e.g., the Sun) may have a mix of continuous spectrum, absorption lines, and emission lines.

• If we know distance and rate at which we receive energy, can get rate at which object emits energy.
• From wavelength of maximum emission, get estimate of temperature.
• From detailed spectrum, with emission and absorption lines, learn about chemical composition, more about temperature.
• Can also learn about object's velocity towards or away from us, from Doppler shift (more later).
A complication for objects in solar system: much of light is reflected from Sun, not emitted by body.