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So here we are in 1913 (just a mere 105 years ago at the time of this writing). What did Bohr know? He knew:

1 That a hydrogen atom is the simplest atom, consisting of just one proton (positively charged) and one electron (negatively charged).

2 That all of the atom's mass is concentrated at the core: that is, the proton.

3 That electrons are negative particles somehow orbiting the nucleus.

4 That the great majority of space in an atom is empty.

5 That all the other elements can be organized neatly by weight on a periodic table.

6 That all elements have different emission spectra with specific emission or absorption color lines.

Niels Bohr (1885–1962, Figure 1.12) was able to beautifully explain all of these observations and how the spectral lines are generated. He postulated in 1912 that an atom consists of a core nucleus that has all the mass and is surrounded by electrons, moving like a planetary system in well‐defined orbits (Figure 1.13). Electrostatic forces between the proton and the electron (analogous to the gravitational forces in the solar system) keep the electrons circulating without escaping their orbit. Additionally, Bohr postulated that the electrons in orbit do not radiate any energy, so the orbits are stable. The only way to radiate or absorb any energy is for an electron to jump from one orbit to another, and that is precisely what explains the spectra of hydrogen and other elements.

Figure 1.12 Niels Bohr (left) postulated the planetary model of the atom. Wolfgang Pauli (right), using quantum mechanics, proved that no two electrons in a system can have the same quantum numbers.

Source: Wikipedia, https://en.wikipedia.org/wiki/Niels_Bohr#/media/File:Niels_Bohr.jpg (left); Wikipedia, https://en.wikipedia.org/wiki/Wolfgang_Pauli#/media/File:Pauli.jpg (right).

Figure 1.13 The Bohr planetary model of an atom has discrete and stable orbits. An electron falling from level 3 to level 2 transfers its energy to an equivalently energetic photon.

Since electrons are forbidden to have any energy except for the energy of a specific orbit, they have to jump from one orbit to another, like going up the stairs, one, two, or three steps at a time (not one and a half). When falling from a higher orbit to a lower one, the electron releases a fixed packet of energy in the form of a photon of a very precise frequency (remember that Einstein said light behaves like a particle with an energy related to the wavelength of the light: Eq. 1.5). The transition from orbit 3 to orbit 2, as I show in Figure 1.13, results in the emission of a photon of a very precise frequency, given by the change in energy, ΔE, divided by Planck's constant. Similarly, if an electron in orbit 2 wants to jump to orbit 3, the hydrogen atom has to absorb the energy it needs by absorbing a photon with the same precise energy, or by thermal heating, or by some other means. All other light photons not exactly matched to the difference between the energy levels go through the material unimpaired. The material is therefore transparent for all of the light waves that do not match the exact difference between two energy levels.

In 1924, Austrian Wolfgang Pauli (1900–1958, on the right in Figure 1.12) proposed his exclusion principle, which states that no two electrons (or fermion particles) in a system can have the same quantum numbers. The first atomic level of any element can hold only 2 electrons, the second 8, the third 18, the fourth 32, etc. A simple relation tells you how many electrons can share a given energy orbit: 2n². You may wonder why. If, according to Pauli's exclusion principle, the electrons cannot share the same quantum state, why do we have more than one electron in each orbit? The answer is that each electron is described by four quantum numbers (like the three numbers that describe your first, middle, last names, and your date of birth), but only the first quantum number, n, specifies the energy of the electron and thus explains the behavior of the light spectra. I explain the electron's four quantum numbers in more detail in Appendix 1.1.

Here's an analogy. Suppose I have a theater with 2 seats in the first row, 8 in the second, 18 in the third, 32 in the fourth, etc. The tickets for the first row cost $20, the second row $50, the third row $75, the fourth $125, and so on. (I know, it is a weird theater, but this is just an analogy.) Spectators are forbidden to sit in someone else's lap or stand in the aisles. If 12 people show up for the performance, they first occupy the 2 seats of the first row, the next 8 patrons occupy the second row, and the last 2 spectators sit somewhere in the third row. Further back in the theater, the rows have more seats, but they are empty. If a patron wants to change rows – from row 3 to row 4, for example – he has to pay the extra $50: the difference in the price of the tickets in the different rows. If he moves the other way, from row 4 to row 3, he is reimbursed the $50. Now, if a wealthy person in row 1 wants to move to row 4, he will be required to pay $105. That is, money must be paid or received to move from one row to another. All these changes assume that the seat someone desires is unoccupied. If the group of spectators is short of money (no energy), they will occupy the seats of the first rows as long as there are seats available. If the group is wealthy (has lots of energy), they can jump from one seat to another as long as they have enough money (energy) to afford the higher prices. The amount they have to pay depends only on the difference in the price of the seats in each row. End of analogy.

At 0 K, absolute temperature (−273 °C), there is no energy whatsoever, so all the electrons occupy the lowest allowed energy levels. At room temperature, 300 °C, there is quite a large amount of thermal energy, and electrons start moving from one level to another, leaving empty seats that can be occupied by other electrons, absorbing or emitting photons as they move.

Figure 1.14 shows the transitions observed in the hydrogen atom. The groups of lines were named later by those who found them.

Have you ever wondered why, when we walk on the second floor, we do not fall through it and land on the first floor? Think about it. The typical size of an atom is 5 × 10⁻¹⁰ m, and the size of a nucleus is about 30 000 times smaller, 1.6 × 10⁻¹⁵ m. All the mass is concentrated in the nucleus. The atoms are, for all practical purposes, composed of empty space. So why does the empty space of my shoes do not go through the empty space of the tiles on the second floor? It is not due to electrostatic repulsion. Both the soles of my shoes and the tiles are electrically neutral. The reason we do not fall through the floor is the Pauli exclusion principle. The electrons in the sole cannot find a lower energy level on the atoms of the tile. The Pauli exclusion principle not only keeps us safe on the second floor but also explains why material physical objects have any volume at all. It also explains friction. The atoms of the sole locate themselves in a preferential position with the atoms of the floor, and they resist moving. How intense the friction is depends on the crystallographic structure of the two surfaces (Emily Conover, “Giving Friction the Slip”, Science News, 3 August 2019).

Figure 1.14 The observed energy lines of the hydrogen atom corresponding to all the transitions between different atomic levels.

In the next chapter, I discuss how these single unique energy levels that Bohr postulated explain the electric properties of different materials.