1.
It turns out that electrons and beta particles are the same thing! OK, strictly speaking, beta particles can be either electrons or anti-electrons (a.k.a. positrons), particles which have the mass of an electron but a positive charge.
2.
A small but significant number of alpha particles -- about 1 in 8000 -- was scattered by 90 degrees or more: sideways or backwards. Now, people had thought that atoms were positively charged spheres in which a number of negative electrons were embedded. British physicists called this the "plum pudding" model; Americans can substitute "raisin pudding" or "raisin bread." The "raisins," of course, were the electrons.
But a spread-out positive "pudding" would never be able to deflect alpha particles very much. Only a strong concentration of positive charge within a gold atom could do that. This, Rutherford realized, is the nucleus -- and the rest of the atom is mostly empty.
3.
Photons have no mass, but they do have energy (which is proportional to the frequency of the corresponding electromagnetic wave).
Since photons are light, they certainly do travel at the speed of light -- and they certainly can be seen (at least, in the visible range).
4.
Opaque bodies glow -- they're incandescent. The hotter they are, the brighter they are, and the shorter the wavelength at which the bulk of their light is emitted. If you prefer, you can say that the frequency gets higher, or that the typical photon becomes more energetic.
By the way, I mentioned "size" because a huge cool opaque object can actually be more luminous than a tiny hot one. This is the idea behind the astronomical objects known as red giants and white dwarfs.
5.
The stopping voltage is the voltage required to prevent even the fastest photoelectrons from reaching the collector plate and completing the circuit. Hence it tells us the maximum kinetic energy of the ejected electrons. For instance, a stopping voltage of 2.5 V means that the photoelectrons are ejected with no more than 2.5 eV of kinetic energy.
The other measured quantity is the photocurrent (in amperes, or coulombs per second). This tells us how many electrons leave the metal each second, but not how much energy they have when they leave the metal.
6.
If light is an electromagnetic wave -- a pattern of oscillating electric and magnetic fields -- then even if the oscillation is at low frequency, the wave can carry lots of energy simply by having a large amplitude. In other words, you can have a strong electric field which points first one way, then another. This corresponds to an intense (bright) light beam, and some of this wave energy should be available to liberate electrons from the metal.
Since it doesn't work this way when you actually run the experiment, light clearly isn't just a wave.
7.
All that influences the kinetic energy of the photoelectrons is the frequency or wavelength of the light waves hitting the metal plate. Energetic photons correspond to short wavelengths or high frequencies.
Increasing the brightness without changing the wavelength means that more photons are absorbed by the metal each second, but each of these photons has the same energy as before; hence the photoelectrons have the same kinetic energy as before.
Now, if we send in a 3.1 eV photon, we still use up at least 2.9 eV removing an electron from the metal, leaving no more than 0.2 eV for this electron's kinetic energy.
10.
Thomson deflected the electrons using electric and magnetic fields. For given field strengths, greater charge produces greater forces and hence a more curved path for the electrons; but greater mass means more inertia, greater tendency to keep moving in a straight line, and hence less deflection. So if an electron shows strong deflection -- a tightly curved path -- that means that it has large charge, small mass, or both; that is, it tells us that the ratio of charge to mass is large.
(Actually the amount of magnetic force also depends on a third variable, the electron's speed. Thomson could indeed figure out how fast his electrons were moving, but I won't go into that here.)
11.
Brownian motion is the random motion of a microscopic particle in suspension. Robert Brown first observed this phenomenon for pollen grains suspended in water; it can also be observed for smoke particles suspended in air. Water molecules are submicroscopic and hence too small to see; beach balls are macroscopic (bigger than a breadbox) and hence too large for this effect to be noticeable. Fish may indeed move randomly but that has nothing to do with physics. . . .
12.
In 1905 Einstein published two papers (out of five total in that "miracle year") that analyzed Brownian motion. The mystery was that microscopic particles (e.g., pollen grains) were randomly jerking about -- accelerating -- despite the apparent absence of any force acting on them, contrary to Newton. (Additionally, this constantly changing motion appeared to be some weird kind of perpetual motion, something that was known to violate the laws of thermodynamics.) Einstein's explanation was that submicroscopic particles (e.g., water molecules) that we can't see are banging into the microscopic particles that we can see, hence the random motion.
For a large object, such as a beach ball floating in water, equal numbers of collisions would happen on opposite sides of the object, so the forces would cancel out. But for a microscopic object like a pollen grain, there won't be that many collisions per second, so there might be a few more collisions on one side than on the other -- in much the same way that flipping a coin only four times might yield three heads and one tail rather than two heads and two tails. The forces don't cancel, and thus the pollen grain should jerk around like a drunkard taking a "random walk." It is characteristic of such random motion that the distance traveled away from a starting point does not increase proportionally to the time spent traveling (as it would for steady motion) but instead as the square root of the time. For example, if a drunkard takes 100 steps in random directions, he (or she) is most likely to end up only 10 steps away from the starting point: 10 is the square root of 100. An experimental physicist by the name of Perrin made careful measurements of suspended gum particles -- carefully selected to be all the same size, since the particle size matters -- and showed that this prediction of Einstein's was correct. After this, no one could doubt the reality of atoms and molecules.
13.
Neither choice is correct, actually: Thomson was able to measure e/m, the charge-to-mass ratio of the electron, but was not able to measure either one of these two quantities individually. To simplify enormously, he used an electric field to deflect electrons, and the amount of deflection is proportional to the electron charge (more charge = stronger response to the electric field) and inversely proportional to the electron mass (more mass = more inertia = less acceleration = less bending). Actually the electron's speed also matters, but he was able to determine this speed by then applying a magnetic field to cancel out the deflection due to the electric field; this works because the magnetic force on a moving charged particle depends not only on the magnetic field but also on the particle's speed.
Thomson's electrons underwent surprisingly large deflections, indicating that they had large charge-to-mass ratios: either very large charge or very small mass. About a decade later someone measured the electron charge e, at which point it became clear that it's the mass m that's very small.
14.
The third choice is correct. In order to explain why blackbodies emit little ultraviolet radiation unless they are very hot, Planck was forced to assume that they can only emit UV light in high-energy "chunks" or "increments" (my terms, not his). A cool blackbody has mostly slow-moving atoms, each of which lacks the energy to emit even one such burst of UV light -- so they must instead settle for emitting none at all.
Note that this is not the same as Einstein's later concept that the light itself can only exist as particles ("quanta") that have fixed energies -- high for ultraviolet light, low for infrared light. Einstein described the difference between the two concepts as follows: Planck's hypothesis was equivalent to saying that a pub can only sell beer in one-pint quantities; whereas Einstein was going further and saying that beer can only exist in one-pint increments, that it's impossible for, say, 1.7 pints of beer to exist. Saying that atoms can only emit high-energy bursts of UV light doesn't mean that UV light can only exist in discrete high-energy units. Planck, and virtually every other physicist, thought that Einstein was flat-out wrong to make that additional claim.