Review: Why Atoms?

• Chemical combination rules (Dalton)

• Success of kinetic theory in describing behavior of matter– Predictions that follow from the theory are confirmed, although

atoms are not “directly” observed

• Brownian motion– A way of seeing atoms “directly”

– Again, predictions based on atomic theory are confirmed by experiments

• X-ray diffraction– Studied in detail in the early 20th century

How Big are They?

• Clearly, very small!

• Too small to be visible in the best optical microscopes– Microscopes can only resolve an object that is comparable in size

or larger than the wavelength of the light used to illuminate it

– For visible light, the smallest structures that can be seen are about 400 nanometers, or 4 10–7 m

– Atoms must be smaller than this!

What is Light?

• Light is a type of wave

• Other common examples: water waves, sound

• A wave is a disturbance in a medium (water, air, etc.) that propagates

• Typically the medium itself does not move much

Anatomy of a Wave

Electromagnetic Waves

• Medium: the electric and magnetic field

• Speed = 3 105 km/sec (about 186,000 mi/sec)

The Electromagnetic Spectrum

Visible Light

• The color of visible light is determined by its wavelength

• White light is a mixture of all colors

• We can separate out individual colors with a prism

Visible Light

400–440 nm Violet440–480 nm Blue480–530 nm Green530–590 nm Yellow590–630 nm Orange630–700 nm Red

1 nm = 1 nanometer = 10–9 m

Longer wavelength Shorter wavelength

Superposition and Interference

• When several waves pass through the same place, the total wave is obtained by adding together the individual wave displacements (Principle of Superposition)

X-Ray Diffraction

• X-rays have wavelengths comparable to atomic sizes

• We can “see” atoms and molecules by bouncing X-rays off them

• Crystals and molecules reflect X-rays in patterns depending on their structures

• From the reflection pattern one can figure out the structure!

X-ray diffraction pattern of DNA

Interaction of X-Rays with Atoms

• Involves the electrons, primarily

More Information

• Intensities (brightness) of diffraction maxima can vary – more information about detailed structure

• The symmetry of the crystal structure is reflected in the diffraction pattern

So, How Big are They?

• Earliest estimate: Johann Loschmidt (1865)– Used results from kinetic theory to estimate

the size of an “air molecule”• We no know there are several types of

molecules present in air

• They are roughly the same size, though!

– His result was about one millionth of a millimeter

• In other words, about 10–3 m/106 or 10–9 m

• This is about 400 times smaller than the smallest object visible in an optical microscope

Brownian Motion

• Discovered in 1828 by Robert Brown, a Scottish botanist

• He observed that microscopic pollen grains suspended in a liquid move around erratically, even though the liquid itself has no observable motion

• Explanation: the grains are being jostled and buffeted by unseen atoms

• The smaller the grain, the more violently it is agitated

Size of Atoms

• In 1905, Einstein worked out several predictions regarding Brownian motion using atomic theory

• Confirmed by Jean Perrin (1908)– Nobel Prize for Physics 1926

• Based on his measurements, Perrin gave an accurate estimate of the size of atoms: about 1-2 10–10 m

• The atomic scale is about a tenth of a nanometer

Avogadro’s Hypothesis

• Equal volumes of gases under the same conditions of temperature and pressure have equal numbers of molecules

• Derived from the observations by Gay-Lussac and others– gases unite in simple proportions by volume

– if a reaction of two gases produces a gas, the volume of gas produced is also related by a simple proportion

• He also proposed that some gases (like oxygen and hydrogen) are not made up of single atoms

• Why weren’t his idea quickly accepted?– they indicated that Dalton’s atomic weights were wrong

– there was no agreement as to what a “molecule”

– he was not a particularly accomplished experimentalist

Loschmidt’s Number

• Avogadro’s Hypothesis predicts that one cubic centimeter of any gas under standard conditions will always contain the same number of molecules

• Avogadro, however, never calculated this number (he had neither the experimental or theoretical background to accomplish this)

• The first estimate of this quantity was made by Loschmidt in 1865 from the kinetic theory of gases

• (Cannizzaro first promoted Avogadro’s ideas at the Karlsruhe Conference of Chemists in 1860)

Avogadro’s Number

• Chemists prefer to use what we now call “Avogadro’s Number” for many calculations

• Avogadro’s number is the number of oxygen (O2) molecules in 32 grams of oxygen, or the number of H2 molecules in 2 grams of H2

or the number of molecules per mole of molecules• It is an honorary name (first used by Perrin in

1909) – still called Loschmidt’s Number in Germany

• NA = 6.022 x 1023 (atoms or molecules) per mole

Estimating Avogadro’s Number