Answers to Idea 4 Study Questions -- 7 Ideas Sec. 005

(1) From around 1905 to the present. It is a pretty modern theory.

(2) Some of them:

(a) Photoelectric effect

(b) Atomic Spectra

(c) Black Body radiation

(3) Under certain conditions (namely, high enough frequency light), if I shoot light at some metals, electrons fly off of them.

(4) Nothing - IR light is low frequency and will not kick off electrons (not enough energy).

(5) Einstein stated that

(a) light is made of bundles of energy (called photons)

(b) the energy of a photon is solely dependent on the frequency of the light.

Thus, for example, infrared light photons have very low energy and cannot kick out an electron, while blue light has more energy and can do so.

(6) If you make a gas glow by providing energy from, e.g., electricity, then the atoms of gas emit light of various distinct colors, the "spectrum" of that particular gas. Technically, this is actually the "emission spectra" of the gas - there is also an "absorption spectra".

(7) Both people before Bohr and after might have said that the electrons simply orbit the nucleus (held on by electric forces). Bohr made the assumption (very important) that only *certain orbits* are allowed - thus only certain energies are allowed for the electrons, the allowed "quantum states".

(8) Bohr's model worked quite well for hydrogen - but not for anything else (hydrogen is, of course, the simplest atom - only 1 electron. His model failed even for helium with 2 electrons).

Thus it was sort of a hint of the right theory, but not so great on its own.

(9) Suppose I give an electron some energy - then, if I give it the right amount, the electron will go into some other allowed orbit. When the electron falls back to a lower energy orbit (this happens for a couple of different reasons), the extra energy is emitted as a photon. Now, the energy of this photon must simply be the difference in energies of the excited (extra energy) orbit and the one the electron falls back into - thus you will get different energy (frequency, color) photons depending on how much energy you gave the electron and which orbit it decides (for whatever reason) to fall back into. Get it? If not, see me and/or the book.

(10) de Broglie noticed something odd - if you assume that some sort of wave is associated with an electron, then, by also assuming that an integer (1,2,3,4,…) number of wavelengths fit around the atom (roughly speaking, so that the electron always returns to the same place after one orbit), one gets exactly the same allowed orbits as Bohr calculated. This, like Bohr's original theory, was sort of a hint that some sort of "wave" was associated with objects.

(11) The bigger the momentum, the smaller the wavelength.

(12) Schrödinger's theory says that for a given object, at each point in space and time, there is a number. This collection of numbers is called the "wave function" of the object and, as its name suggests, mathematically behaves much like a wave (if you want an analogy, we can say that there is a number, the height of the water, associated with every point on an ocean at each moment of time. This is a conventional wave, not a quantum mechanical wavefunction, of course.)

(13) The wave function tells you something bizarre - it tells you the *probability* that the object is located at that particular point of space at that time. Furthermore, according to quantum mechanics, that is *the best you can do* - you cannot say that the object is definitely anywhere, just the probability that it is somewhere.

(14) The wavefunction of an object can penetrate barriers that would stop that object in Newton's world - e.g., like rolling a ball at a hill so softly that it can't go over. Since, quantum mechanically, the wavefunction will generally penetrate through the hill (though it may get small), the ball can appear on the other side of the hill!! In a sense, this is like walking through a wall.

(15) Quantum effects usually only become noticeable for tiny (small mass/momentum) objects like electrons and so on, and so we don't actually walk through walls in everyday life. There are, however, so-called macroscopic quantum phenomena, but these are sufficiently unusual that they are usually only seen in labs.

(16) In Schrödinger's picture, the electrons do NOT orbit the nucleus - the electronic wavefunctions (that tells us the probability that the electron will be in a particular place) is sort of "smeared out" around the nucleus, and even inside it! The actual shape of the wavefunction is precisely calculable from Schrödinger's theory (at least for fairly simple atoms - you need a big computer!). The book has some drawings - see p. 296.

(17) Wonderfully! And, if you include special relativity, it works amazingly well in many, many circumstances. Interestingly, nobody yet knows how to combine *general* relativity, Einstein's theory of gravity, with quantum mechanics.

(18) A number that tells you how magnetic an electron is. This number is predicted amazingly well by a combination of quantum mechanics and relativity (called Quantum Field Theory).

(19) Well, Schrödinger's wave function behaves much like a wave - de Broglie's early work was the first hint of the wavefunction, and his formula for the dependence of the wavelength on momentum is still good.