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?

According to classical physics, an electron orbiting the nucleus should continuously lose energy by emitting light and end up spiralling into the nucleus in a fraction of a second: Rutherford's model rendered atoms unstable.

1. a) What did Bohr postulate about "stationary orbits" to prevent this catastrophe?
2. b) What does it mean that Bohr introduced a "postulate" instead of deducing it from known laws? What justifies accepting a new postulate in science?
3. c) What experimental fact, inexplicable by Rutherford's model, was indeed explained by Bohr's model thanks to its energy levels?

In $1913$, Niels Bohr applied the new quantum ideas to the hydrogen atom. Explain what Bohr postulated about electron orbits and what happens, according to his model, when an electron jumps from a permitted orbit to a lower one.

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?

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.

Fireworks owe their colours to the salts they contain: strontium produces red light, sodium yellow, and copper blue-green. When heated, each element emits light of characteristic colours that form its emission spectrum. Explain what an element's spectrum is and why it is said to be like its fingerprint.

In $1868$, while studying the spectrum of sunlight during an eclipse, a yellow line was observed that did not correspond to any element known on Earth. It was proposed that it belonged to a new element, named helium, from the Greek helios, "Sun".

1. a) Explain how it is possible to know the chemical composition of a star without bringing back samples from it.
2. b) How does this discovery relate to the idea that each element possesses a characteristic spectrum?

The Balmer series of hydrogen satisfies the formula

$\frac{1}{\lambda} = R_{\text{H}}\cdot\left(\frac{1}{2^2} - \frac{1}{n^2}\right)$, with $R_{\text{H}} = 1,097\cdot10^{7}\ \text{m}^{-1}$ and $n = 3, 4, 5\dots$

1. a) Calculate the wavelength $\lambda$ for $n = 3$ and express it in $\text{nm}$. What colour of the visible spectrum does it approximately correspond to?
2. b) Repeat the calculation for $n = 4$.
3. c) What happens to the wavelengths as $n$ increases? Calculate the limiting value for $n \rightarrow \infty$ and explain why the lines in the series get closer and closer together.

On a timeline in the physics classroom, the following milestones appear out of order: Rutherford's model ($1911$), Dalton's model ($1808$), Bohr's model ($1913$) and Thomson's model ($1897$). Order the four models from oldest to most recent and write the popular name by which Thomson's model is known.

A popular science magazine publishes four quotes without mentioning who wrote them. Attribute each one to Dalton, Thomson, Rutherford or Bohr:

1. a) "The atom is a solid, indivisible sphere."
2. b) "The atom is a sphere of positive charge with electrons embedded in it."
3. c) "The positive charge and almost all the mass are concentrated in a tiny nucleus."
4. d) "Electrons can only occupy certain orbits, with well-defined energies."

In $1932$, Chadwick bombarded beryllium with $\alpha$ particles and obtained highly penetrating radiation that was not deflected by electric fields and was capable of knocking protons out of a paraffin block: he had discovered the neutron. The experimental set-up is shown in the figure.

1. a) Why is uncharged radiation not deflected by electric fields?
2. b) Explain why the neutron was much harder to detect than the electron or the $\alpha$ particle.
3. c) Known nuclei weighed more than twice as much as they would if they only contained protons: explain how the discovery of the neutron resolved this problem with the nuclear model.