Behind the Constants Trivia Quiz

Answer: e

Leonhard Euler, a Swiss mathematician who did most of his work for the Russian Czars in St. Petersburg, lived from 1707 to 1783. A child prodigy, his productivity throughout his life was incredible, even during the last 17 years of his life when he was entirely blind (this was well before the invention of Braille). In fact, it took the St. Petersburg Academy 50 years after his death to prepare and release all of the work he had left unpublished!

The number e, critical to any scientific discussion of oscillations or exponential growth or decay, is equal to 2.71828... Euler realized that this number was related to sine and cosine functions: e^(i x) = cos(x) + i sin(x). This formula leads to one that physicist Richard Feynman once called "the most remarkable formula in mathematics": e^(i*pi) + 1 = 0, which relates the five most fundamental mathematical constants.

Answer: Avogadro's number

It was Amedeo Avogadro's work that led to the definition of a mole as 6.022 x 10^23 molecules. Born in Turin in 1776, he became Count of Quaregna at the tender age of 11. He was trained as a lawyer but didn't like it and turned to Mathematical Physics instead.

His brilliant and important idea, that gases are made up of a quantifiable number of atoms and molecules, was published in 1811 and ignored completely during his lifetime (he died in 1856). In the 1880s, however, Avogadro's memory was vindicated when Stanislao Cannizzaro used his work to create a table of atomic weights. Now his work has even led to a very minor holiday: many chemists, especially students anxious for a party, celebrate Mole Day on October 23.

Answer: Faraday constant

Michael Faraday (1791 - 1867) had little formal education; instead, he learned science during his apprenticeship to a bookbinder, consulting the very volumes he was binding. He won a job as a laboratory assistant through tenacity, charm, and the generosity of Sir Humphry Davy, then the President of the Royal Society, and soon made a name for himself with his brilliant experiments. In addition to his studies of conductors and magnetism, he discovered the chemical benzene and invented the system of oxidation numbers still used by chemists today. Famously humble, he declined both knighthood and the presidency of the Royal Society, and he had but three words of advice to aspiring chemist William Crookes: "Work. Finish. Publish."

The Faraday constant is approximately equal to 96,485 Coulombs per mole.

Answer: Stefan-Boltzmann constant

The Stefan-Boltzmann constant has the value 5.67 x 10^-8 Joules per second per area, per Kelvin to the inverse power of four. Stefan (1835-1893) formulated it as an empirical law; his student, Ludwig Boltzmann, derived it theoretically, so the law and constant bear both of their names.

In his youth, Stefan seriously considered becoming a Benedictine monk, but his love for physics was too strong for him to go into the cloister. This was a fortunate decision for physics, because the Stefan-Boltzmann law paved the way for Max Planck's theory of quantized light -- which in turn was the beginning of quantum mechanics.

Answer: Boltzmann constant

Ludwig Boltzmann (1844-1906) made many other important contributions, including the derivation of Stefan's empirical (based on experiment) law for blackbody radiation (see Question 4). He basically derived all of statistical mechanics separately from Gibbs, and he was the first to recognize that entropy must always increase -- now known as the second law of thermodynamics. But other physicists doubted him, and this ate away at his self-confidence. Boltzmann, who likely suffered from bipolar disorder, hanged himself believing his life's work to be in ruins, unaware that the data that would vindicate him was even then being analyzed. His famous equation for entropy is engraved on his tombstone.

The Boltzmann constant is equal to 1.38 x 10^-23 Joules per Kelvin.

Answer: Planck's constant

Max Planck's (1858-1947) naysaying professor was Philipp von Jolly. Planck's theory of blackbody radiation (which is, to a good approximation, the radiation of a star) is now considered to be the cornerstone of quantum mechanics; he won the Nobel Prize in Physics for it in 1918. A proud German physicist at a time when the great work in physics was all being done in Germany, he fought a losing one-man battle against the exile of Jewish physicists as the Nazis took power. For daring to teach the theories of Einstein, he was accused of being a "white Jew" by proponents of "Aryan physics" (whatever that was supposed to be), and the government investigated his racial background. His last surviving child, Erwin, was executed in 1945 for his participation in an assassination attempt on Hitler.

The Planck constant is represented by h = 6.626 x 10^-34 Joule seconds. In quantum mechanics we often divide h by 2pi to get the useful quantity hbar (a lower-case h with a crossed stem).

Answer: Rydberg constant

Johan "Janne" Rydberg (1854 - 1919) was first hired by Lund University as a docent in mathematics, but it was in physics that he made his mark. His formula allowed spectral lines to be related to each other as a predictable series; this is still a guiding principle of atomic physics today. Each emission line is due to photons emitted when an electron "jumps" from a higher-energy orbital to a lower-energy one, so each element has a distinct spectrum and a distinct Rydberg constant R. The Rydberg constant for hydrogen is equal to the energy of the ground state: -13.6 electron volts.

Although his formula revolutionized atomic physics, Rydberg's colleagues were reluctant to laud his accomplishments because he wasn't enough of an experimentalist for their tastes; they trivialized his insight as simply being a rearrangement of other people's data. He lost a contentious tenure fight at Lund University and was denied membership in the Royal Swedish Academy of Sciences, although he was named a foreign member of the Royal Society of London a few months before his death of a brain hemorrhage.

Answer: Bohr radius

Neils Bohr (1885 - 1962) was a Danish physicist who has gone into legend. The Bohr model of the atom, surprisingly accurate and still taught in chemistry classes before students are ready for the more accurate quantum model, was a major advance in the development of quantum physics. It was he who explained, using his model, the emission of photons that Rydberg had studied empirically (Question 7).

Bohr's political views -- which basically boiled down to the idea that all scientific knowledge should be shared across borders -- became controversial during World War II, when Hitler was pushing his scientists to develop nuclear weapons. Werner Heisenberg visited Bohr to try to persuade him to join the project, a conversation that is the subject of Michael Frayn's acclaimed play "Copenhagen". Bohr wound up fleeing Denmark with the aid of the OSS, one step ahead of the German police, and did some minor work for the Manhattan Project.

The Bohr radius, usually represented by a0, is roughly equal to 53 picometers.

Answer: Hubble constant

Edwin Hubble (1889 - 1953) had his first taste of fame in high school, when he set an Illinois state record for the high jump (and won seven first-place prizes at a single track meet). His contributions to astronomy, however, proved longer-lasting. In 1924, he was the first to realize that the controversial "fuzzy nebulae" were actually other galaxies, and by 1929 he and Milton Humason had realized that the more distant galaxies were rapidly receding from our own. They formulated Hubble's law: v = H0 * d, where v is a galaxy's recessional velocity, d its distance from the Milky Way, and H0 the Hubble constant (71 kilometers per second per Megaparsec). This is an incredible result: the farthest galaxies are receding from us at the greatest speed! Thus, the first real evidence that our universe is expanding.

Hubble also discovered the odd comet or two, formulated a classification scheme for galaxies based on their geometry, and lobbied extensively for astronomy to be considered a subfield of physics, so that astronomers could be recognized with Nobel Prizes. His campaign was successful but took too long: Hubble died just after the Nobel Committee had unanimously decided to honor him, but just before they could award him the prize.

Answer: Chandrasekhar limit

Subrahmanyan Chandrasekhar (1910 - 1995) was born in Lahore in what is now Pakistan, the son of a Brahmin family and the nephew of Nobel Physics laureate Chandrasekhara Venkata Raman (who won the prize for his discovery of the Raman effect in the scattering of monochromatic light). In order to pursue his studies of physics he had to leave India, creating a cultural conflict that dominated his early years. Despite his arrival with his seminal white-dwarf theory in hand, his reception at Cambridge was less than warm, and after getting his PhD he left for the United States and the University of Chicago (eventually becoming a naturalized citizen).

Nicknamed Chandra (Sanskrit for "moon" or "luminous"), his later work included fundamental theories of radiative transfer, fluid and plasma physics, gravitational theory and stellar evolution, and he was thus understandably upset that his Nobel prize made no mention of any work he had done after his early 20s.