Review: Why Atoms?

1. 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

2. 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!

3. 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

4. Anatomy of a Wave

5. Electromagnetic Waves • Medium: the electric and magnetic field • Speed = 3  105 km/sec (about 186,000 mi/sec)

6. The Electromagnetic Spectrum

7. 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

8. Visible Light 400–440 nm Violet 440–480 nm Blue 480–530 nm Green 530–590 nm Yellow 590–630 nm Orange 630–700 nm Red 1 nm = 1 nanometer = 10–9 m Longer wavelength Shorter wavelength

9. 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)

10. 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

11. Interaction of X-Rays with Atoms • Involves the electrons, primarily

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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 • (Cannizzarofirst promoted Avogadro’s ideas at the Karlsruhe Conference of Chemists in 1860)

18. 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 H2or 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

19. Estimating Avogadro’s Number