Recap: 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 20 th century

Response Sheet Questions Are scientists and philosophers really at odds? Isn’t it true that science is, in part, a collection of facts? Why would the Royal Society refuse to open the notebooks in Popper’s fable? Who was Joanna Southcott? Relation between the arts and sciences, and mutual influences?

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  10 5 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 nmViolet 440–480 nmBlue 480–530 nmGreen 530–590 nmYellow 590–630 nmOrange 630–700 nmRed Longer wavelength Shorter wavelength

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/10 6 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

Making Predictions for Brownian Motion Question: How far does the grain move (on average) in some time T? Assumptions: 1.The grain is buffeted on all sides by unseen particles 2.Due to statistical fluctuations, there is occasionally an excess of collisions on one side of the grain, leading to a slight “kick” in the opposite direction 3.The direction of the kicks is random, i.e. the direction of one kick is independent of any previous kicks 4.On average, these “kicks” occur every T 0 seconds 5.On average the kicks are the same “size”, i.e. they cause the same displacement of the grain

Model Calculation “Random walk” (one dimensional, for simplicity) Grain starts at square 0 Each step corresponds to a “kick” For each step, flip a coin –Heads, go right –Tails, go left Do it many times and see how far the grain has gotten after N steps, on average 0

How do we work it out? Could flip many coins, but easier to let a computer do it! –It never gets tired or bored So we let the computer –Flip virtual coins and determine how far the grain gets after N steps –Repeat a large number of times –Calculate the average distance traveled in N steps –Then repeat for some other value of N How does the average distance D change with N?

The Result The average distance is proportional to the square root of N Since each step took T 0 seconds, the total time taken is Hence Confirmed by Perrin!

The Electromagnetic Spectrum

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

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 (O 2 ) molecules in 32 grams of oxygen, or the number of H 2 molecules in 2 grams of H 2 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 N A = x (atoms or molecules) per mole

Estimating Avogadro’s Number