*Reference: A Logical Approach to Theoretical Physics*

## PART XI – ATOMIC THEORY DEVELOPS

#### THE WORLD OF ATOM by Boorse

## Chapter 54: Atomic Number (Henry G. J. Mosley 1887 – 1915)

It seemed to Mendeleev that the mass of an atom is the decisive physical parameter that determines its structure and chemical behavior. Mosley thought that if the electrons were moving in orbits according to the Bohr theory, the X-ray spectrum of a heavy element should exhibit a line structure similar to that of the hydrogen spectrum. The X-ray spectrum would change in a regular way according to charge on the nucleus (the atomic number) as one went from one heavy atom to the next if the Bohr-Rutherford model of the atom were correct.

As the charge increases, the electron orbits become more closely bound to the nucleus and we should expect the frequency of spectral lines to increase. This is precisely what Mosley found—the step-by-step change in the frequencies of two distinct lines as one progresses from the lighter to heavier elements. Mosley stated this relationship in a simple empirical formula, which he was able to match with the data. Mosley’s formula shows that the atomic number and not the atomic weight is the decisive quantity in the arrangement of the elements in the periodic table.

## Chapter 55: Quantum Theory of Radiation and Atomic Processes (Albert Einstein 1879 – 1955)

**The Quantum Theory of Radiation. **Einstein (1917) gave the nuclear atom a logically satisfying structure by deriving the Planck’s radiation formula from the Bohr Theory and stationary states. Einstein showed that radiation is a fully directed phenomenon because the momentum of a quantum must be taken into account. A remarkable aspect of this derivation is the appearance of the stimulated emission process (verified later by the development of Laser).

## Chapter 56: The Compton Effect (Arthur H. Compton 1892 – 1962)

**A Quantum Theory of the Scattering of X-Rays by Light Elements. **The X-ray beam, after it is scattered by electrons, suffers a definite reduction in frequency. Compton showed that energy of the photon, as given by its frequency, is reduced by the same amount that the kinetic energy of the recoil electron is increased. Thus, the photon is a momentum carrying corpuscle that can transfer its momentum in a given direction to the atom. The Compton effect also implies that the electron must be treated as a wave and not as a particle.

## Chapter 57: Space Quantization (Otto Stern 1888 – 1969, Walter Gerlach 1889 – 1979)

**Experimental Proof of Space Quantization in a Magnetic Field. **The fine structure of spectral lines was explained by the quantization of the angular momentum, in addition to the quantization of electron orbits within the atom. Furthermore, there is “space quantization,” which is the concept that the component of the angular momentum vector along the z-direction can take only certain values.

## Chapter 58: Electron Spin (Samuel A. Goudsmit 1902 – 1978, George E. Uhlenbeck 1900 – 1988)

**Spinning Electrons and the Structure of Spectra. **Electron was assumed to be like a golf ball and its spin was postulated to provide the fourth quantum number to explain the complexities of the atomic spectra, but electron can equally be a wave, with “electron spin” requiring a different explanation. Therefore, electron spin is essentially a mathematical parameter.

*The four quantum numbers in atomic physics are: principal quantum number, azimuthal quantum number, magnetic quantum number, and spin quantum number. Together, they describe the unique quantum state of an electron.*

*The principal quantum number (n) indirectly describes the size of the electron orbital. It has the greatest effect on the energy of the electron. It was first designed to distinguish between different energy levels in the Bohr model of the atom. It is always assigned an integer value (e.g., n = 1, 2, 3…), but its value may never be 0. An orbital for which n = 2 is larger, for example, than an orbital for which n = 1. Energy must be absorbed in order for an electron to be excited from an orbital near the nucleus (n = 1) to get to an orbital further from the nucleus (n = 2).*

*The azimuthal quantum number (l) for an atomic orbital determines its orbital angular momentum and describes the shape of the orbital. *

*The magnetic quantum number (m_{l}): m_{l} = -l, …, 0, …, +l. Specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the sub-shell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each sub-shell.*

*The spin quantum number (m_{s}) describes the angular momentum of an electron. An electron spins around an axis and has both angular momentum and orbital angular momentum. Because angular momentum is a vector, the Spin Quantum Number (s) has both a magnitude (1/2) and direction (+ or -).*

## Chapter 59: The Exclusion Principle (Wolfgang Pauli 1900 – 1958)

**Exclusion Principle and Quantum Mechanics. **The four quantum numbers were developed following the Bohr’s model to explain the atomic spectra and to establish consistency among the elements in the Periodic table. Within a given atom, no two electrons can have identical full sets of quantum numbers. The Exclusion Principle has assisted greatly in postulating a structure for the atom. The atomic model is essentially based on a mathematical consistency.

## Chapter 60: Secondary Radiation (Chandrasekhara Venkata Raman 1888 – 1970)

**A New Class of Spectra Due to Secondary Radiation. **When light hits a molecule or an atom, it is scattered. The scattered light contains frequencies equal to, smaller than, and larger than the frequency of the primary light. That part of the incident frequency is absorbed which corresponds to the natural frequency of the molecule, and the rest is scattered, or the natural frequency is added to the incident frequency of the light that is scattered. This is the Raman Effect.

## Chapter 61: Statistical Mechanics (S. N. Bose 1894 – 1974)

**Planck’s Law and Light Quantum Hypothesis. **Bose applied quantum principle of discrete energy levels to Statistical mechanics. The quantum definition takes the identity of the particles into account. It leads to a distribution different from the Maxwell-Boltzmann distribution, and hence to a different equation of state for a perfect gas. Boyle’s law does not hold for such a gas and the departure from Boyle’s law becomes greater and greater as the temperature decreases.

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**MAIN POINTS**

- The charge on the nucleus is represented by the atomic number.
- Elements differ from each other by their atomic number and atomic weight.
- As the charge increases, the electron orbits become more closely bound to the nucleus.
- The atomic number and not the atomic weight is the decisive quantity in the arrangement of the elements in the periodic table.
- The stationary orbits in Bohr’s model are consistent with Planck’s theory of Quantum.
- The momentum of radiation makes it a directed phenomenon.
- The photon is a momentum carrying corpuscle that can transfer its momentum in a given direction to the atom.
- The electron must be treated as a wave and not as a particle.
- The quantization of the angular momentum explains the fine structure of spectral lines,
- The electronic structure around the nucleus is defined by four different quantum numbers.
- Within a given atom, no two electrons can have identical full sets of quantum numbers.
- Lines in spectra occur also due to vibration phenomena other than absorption and emission.
- More mathematical relationships are being worked out for the atomic domain.

**THEORY****The structure of the atom is increasingly the result of mathematical consistency among experimental observations. The mathematical model defines the structure of the substance that is transitioning from mass of the nucleus into the surrounding vortex of energy.**

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