Classical atomic models

When John Dalton proposed his atomic model in $1808$, he imagined atoms as tiny solid spheres. Explain in your own words the two main ideas of his model: what an atom is according to Dalton and how atoms of one element differ from those of a different element.

In $1897$, J. J. Thomson experimented with cathode ray tubes, which are nearly empty glass tubes with two electrodes connected to a very high voltage. A diagram of one of these tubes is shown in the figure.

What particle did Thomson discover through these experiments? What electric charge does this particle have, and where did it come from, according to his interpretation?

In $1911$, Rutherford and his collaborators bombarded an extremely thin sheet of gold foil with $\alpha$ particles, which have a positive charge. What happened to the vast majority of the particles when they reached the foil? What conclusion did Rutherford draw about the inside of the atom?

In the gold foil experiment, three things were observed: most of the $\alpha$ particles passed through the foil without deflecting, a small fraction deflected at large angles, and a very few bounced straight back. The figure summarizes these three observations.

1. a) Write down the conclusion Rutherford drew from each of the three observations.
2. b) What would Thomson's model have predicted for this experiment? Why was this prediction not fulfilled?

The electron discovered by Thomson is a particle that comes from inside atoms, regardless of the element.

1. a) Explain what fundamental idea of Dalton's model was disproved by this discovery.
2. b) If atoms contain electrons, which are negatively charged, but are electrically neutral, what did Thomson have to add to his model to explain this neutrality?

A discharge tube filled with hydrogen glows with a pinkish light which, when viewed through a spectroscope, separates into a few well-defined coloured lines. Observe the set-up in the figure:

1. a) Explain, using Bohr's model, why hydrogen emits only certain colours and not a continuous rainbow.
2. b) What is the relationship between the energy of the electron jump and the colour of the emitted line?

$\alpha$ particles have a positive charge and a mass about $7000$ times greater than that of the electron.

1. a) Explain, using forces between electric charges, why an $\alpha$ particle passing very close to the nucleus deflects significantly, but barely changes its trajectory when passing near an electron.
2. b) Why do the particles that get closest to the nucleus bounce straight back?
3. c) If the gold foil were twice as thick, how would you expect the proportion of particles bouncing back to change? Explain your answer.

Thomson placed two electrically charged plates on either side of the cathode ray tube and observed that the beam deflected towards the positive plate. The set-up is shown in the figure.

1. a) What did Thomson conclude about the sign of the charge of the particles in the beam? Explain your reasoning.
2. b) He repeated the experiment with tubes containing different gases and always obtained the same particles, with the same charge-to-mass ratio. What does this result imply about the electron as a constituent of matter?

According to Bohr's model, the first three energy levels of hydrogen are $E_1 = -13,6\ \text{eV}$, $E_2 = -3,4\ \text{eV}$ and $E_3 = -1,5\ \text{eV}$. When an electron falls from one level to a lower one, it emits a photon whose energy is exactly the difference between the two levels. The figure shows the three levels and the two transitions.

1. a) Calculate the energy of the photon emitted in transitions $E_3 \rightarrow E_2$ and $E_2 \rightarrow E_1$.
2. b) Which of the two photons has higher energy? Knowing that higher photon energy corresponds to a higher light frequency, which of the two emitted lights has a higher frequency?
3. c) Explain, based on these results, why the spectrum of hydrogen consists of discrete lines and is not continuous.

Imagine that Thomson's model were correct and the atom were a soft sphere of positive charge with electrons embedded in it.

1. a) What would happen to $\alpha$ particles as they passed through the gold foil according to that model? Could they ever bounce back? Explain your reasoning thinking about how charge and mass are distributed.
2. b) What observation from the actual experiment proves that model to be false?
3. c) Explain why, for an $\alpha$ particle to be able to bounce back, the positive charge and almost all the mass must be concentrated in a very small space.