of several other materials."/>
Figure 1.6 The spectrum of the hydrogen atom on the left shows the absorption lines (below) and the emission lines (middle). On the right are the emission lines of several other materials.
Source: https://www.shutterstock.com/image‐vector/spectrum‐spectral‐line‐example‐hydrogen‐emission‐1288942888?src=iUiOwiDEznOcV6XzswXhMA‐1‐0 (left); https://www.shutterstock.com/image‐vector/line‐spectra‐elements‐339037577?src=I6tWF1qlh6XcWayXsZl‐Gw‐3‐16 (right).
Figure 1.6 shows the hydrogen spectrum on the left, with its characteristic emission and absorption lines. These are the lines that Balmer used to develop Eq. (1.3) to calculate the missing hydrogen's wavelengths. All the elements have similar absorption and emission lines at different wavelengths, and I show a few on the right in Figure 1.6.
Just three years later, Johannes Rydberg (1854–1919) found that the Balmer equation was one specific case of a more general formula, Eq. (1.4):
The reciprocal of the wavelength is now given by a constant R and the same integer numbers, except that now n is allowed to have different integer numbers: 2, 3, 4, and so on. R is also a heuristically derived constant (R = 1.1 × 107 m−1), called the Rydberg constant. Both Balmer and Rydberg (Figure 1.7) were able to quantify the entire spectrum of the hydrogen atom using the relationship in Eq. (1.4). It is interesting that Niels Bohr, whom I'll talk more about in Section 1.8, was able to calculate the Rydberg number using fundamental physical values, such as the mass of the electron, the electronic charge, the permittivity of free space, Planck's constant, and the speed of light (see Appendix 1.3). This behavior screams for an explanation.
Figure 1.7 Johann Balmer (left) found a mathematical relation for hydrogen's spectral lines, and Johannes Rydberg (right) came up with a more general equation applicable to all gases and materials.
Source Wikipedia, https://en.wikipedia.org/wiki/Johann_Jakob_Balmer#/media/File:Balmer.jpeg (left); Wikipedia, https://en.wikipedia.org/wiki/Johannes_Rydberg#/media/File:Rydberg,_Janne_(foto_Per_Bagge;_AFs_Arkiv).jpg (right).
1.6 Light is a Particle
Albert Einstein (1879–1955, Figure 1.8) published a paper in 1905 on the theory of the photoelectric effect. When light strikes a metal surface, it frees an electron if its energy is higher than a given threshold value. Any remaining energy is used to kick the electron off the surface. In his paper, Einstein proposed the concept that light has a dual personality; it behaves like a wave or like a particle, and the particle has an energy associated with the wavelength of that light.
He called this particle a “light quantum.” (In 1926, a French physicist named Frithiof Wolfers [1891–1971] renamed the light quantum a photon. It is interesting that Einstein received the Nobel Prize in 1921 for the discovery of the photon, not for his much more famous work on relativity.) This light particle, the photon, has an energy that depends on the frequency of the light. The energy associated with this light is given by the formula
where h is Planck's constant (h = 6.63 10−34 m2 kg s−1), c is the speed of light (c = 3 × 108 m s−1), and λ is the wavelength (m). The meter in the numerator cancels the one in the denominator, resulting in the energy given in Joules (= kg m2 s−2).
Figure 1.8 Around 1905, Albert Einstein came up with the concept that light behaves as both a wave and a particle.
Source: Wikipedia, https://en.wikipedia.org/wiki/Albert_Einstein#/media/File:Einstein_patentoffice.jpg.
1.7 The Atom's Structure
While all of these light experiments and relationships were being observed in the late nineteenth century, other scientists were playing with cathode‐ray tubes, the precursors of old television sets and oscilloscopes, trying to understand the nature of the atom. The cathode‐ray tube consists of an evacuated tube with two contacts, one at each end: the cathode and the anode. When a voltage is applied across the tube, current flows from the cathode to the anode, and the tube glows. The scientists explained this phenomenon by saying that electrons going through an evacuated tube containing very few atoms are able to attain sufficient velocity (and therefore kinetic energy) to hit the atoms and make them glow. They were called cathode rays.
Nobel Prize winning British physicist Joseph John Thomson (1856–1940, Figure 1.9) studied cathode rays and postulated in 1897 that they consisted of extremely small negatively charged particles, which he initially called “corpuscles.” (As happened with the term photon, George Stoney (1826–1911) later renamed corpuscles as electrons.) By studying how these particles moved through the gas and how they could be deflected by magnets, Thomson concluded that the “corpuscles” were (i) negatively charged particles and (ii) much smaller than the atoms themselves – at least 1000 times smaller. To account for electrically neutral atoms, he proposed that there is a core of positive charges with a large mass surrounded by an amorphous cloud of negatively charged electrons.
Ernest Rutherford (1871–1937, Figure 1.10), also a Nobel Prize winner, worked with radioactivity. In 1911, he bombarded very thin gold foil with alpha particles and looked at the scattered reflections as the radiation went through the foil. Most of the radiation went through the foil undeflected. Only a few alpha particles were
