he concluded that the atom must have a very small, concentrated, positively charged core to compensate for the negatively charged electrons. Because the large majority of alpha particles passed through the foil without any directional change, he concluded that the majority of the space in an atom is empty, and the electrons are orbiting the nucleus instead of just being a scrambled negatively charged cloud as Thomson had suggested.
Figure 1.9 Joseph John Thomson and his cathode ray tube.
Source: Wikipedia, https://en.wikipedia.org/wiki/J._J._Thomson#/media/File:JJ_Thomson_Cathode_Ray_2.png (left); Wikipedia, https://en.wikipedia.org/wiki/J._J._Thomson#/media/File:J.J_Thomson.jpg (right).
Figure 1.10 Ernest Rutherford, with his experiment that bombarded alpha particles with radiation, concluded that the nucleus is extremely small and is concentrated at the center of the atom.
Source: Wikipedia, https://upload.wikimedia.org/wikipedia/commons/6/6e/Ernest_Rutherford_LOC.jpg.
Robert Millikan (1868–1953, Figure 1.11) was able to measure the electrical charge of an electron with an interesting oil drop experiment in 1909. He suspended a very small charged oil drop between two metal plates – one positive and the other negative – creating an electric field between the plates. He dropped tiny oil droplets into a vacuum chamber, and with X‐rays, he negatively charged some of the oil drops. By changing the electric field between the two plates, he could control the speed of the oil drops, slowing them down, stopping them, or even moving them upward. By knowing the density of the oil drop, the size of the drop, its volume and mass, and the electric field that compensated for the effect of gravity, he was able to come up with the value of the charge of a single electron: 1.592 × 10−19 coulombs (he was off by less than 1% of the now‐established number – not bad at all).
Figure 1.11 Robert Millikan, with his oil‐drop experiment, measured the electrical charge of an electron.
Source: https://en.wikipedia.org/wiki/Robert_Andrews_Millikan#/media/File:Millikan.jpg.
1.8 The Bohr Atom
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