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The Physics Book.

The World of Atom (Part XI)

Reference: A Logical Approach to Theoretical Physics



Chapter 54: Atomic Number – Henry G. J. Mosley (1887 – 1915)
The High-Frequency Spectra of the Elements. The structure and chemical behavior of an atom is determined by the charge on the nucleus rather than its mass. The charge on the nucleus is determined by the number of protons in the nucleus (atomic number).

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 (ml): ml = -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 (ms) 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. 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.


The mathematical consistency provides insight into the structure of atoms that cannot be perceived otherwise.


The World of Atom (Part X)

ReferenceA Logical Approach to Theoretical Physics



Chapter 51: Interference Phenomena – Max von Laue (1879 – 1960) Walter Friedrich (1883 – 1968) Paul Knipping (1883 – 1935)
Interference phenomena for X-Rays. Ingenious idea of using the atoms forming the lattice structure of a crystal as a diffraction grating for X-rays of extremely short wavelength. From X-ray diffraction pattern, one can not only calculate the wavelength of the X-rays but also find out a great deal about the structure of the crystal.

Chapter 52: Bragg’s Law – William Henry Bragg (1862 – 1942) William Lawrence Bragg (1890 – 1971) 
The Reflection of X-Rays by Crystals. This research showed (1) that the X-ray emission spectrum of an element is characteristic of that element, and (2) that X-rays can be used as a powerful and precise means of crystal analysis.

Chapter 53: Atomic Number – Antonius van der Broek (1870 – 1926) 
The Number of Possible Elements and Mendeleev’s “Cubic” Periodic System. The number of the place each element occupies in the periodic table is proportional to the square root of the number of scattered -particles.


The short wavelength of X-rays provides greater insight into the structure of atoms.


The World of Atom (Part IX)

ReferenceA Logical Approach to Theoretical Physics



Chapter 43: Strange Results from -Particle Scattering Hans Geiger (1882 – 1945) Ernest Marsden (1889 – 1970)
On a Diffuse Reflection of the Alpha-Particles. Deflections occurred that were too big to be consistent with Thomson model of atom.

Chapter 44: The Nuclear Atom Ernest Rutherford (1871 – 1937)
The Scattering of Alpha and Beta Particles by Matter and the Structure of the Atom. The large deviations observed experimentally must have been caused by single direct collisions. The alpha particle approached as much as 3 x 10-10 cm close to a point of enormous force in the atom.

Chapter 45: Atomic Structure Niels Bohr (1885 – 1962)
On the Constitution of Atoms and Molecules. Planck’s discovery of the quantum of action and Einstein’s concept of the photon could be combined with Rutherford’s discovery of how  particles are scattered by atomic nuclei to derive a self-consistent planetary atomic model.

Chapter 46: The Quantum Theory is Tested James Franck (1882 – 1964) Gustav Hertz (1887 – 1975)
Collisions between Electrons and Mercury Vapor Molecules and the Ionization Potential of Such Molecules. An atom can take on energy from collisions only in discrete amounts.

Chapter 47: The discovery of Isotopes Frederick Soddy (1877 – 1956)
The Radio-Elements and the Periodic Law. The radioactive transformations produced atoms of the same chemical species but of different weights.

Chapter 48: The Positive Rays J. J. Thomson (1856 – 1940)
Rays of Positive Electricity. There are many different kinds of particles in the positive rays. Development of a method to obtain a mass spectrum.

Chapter 49: Transmutation of an Element Ernest Rutherford (1871 – 1937)
Collision of Alpha Particles with Light Atoms.Nuclei of atoms could be disrupted and changed into other nuclei.

Chapter 50: The Diversity of Atoms Francis William Aston (1877 – 1945)
Positive Rays and Isotopes. Development of mass spectrometers and the discovery of isotopes at the lighter end of the periodic table.



  1. The size of the atom is of the order of 10-8 cm.
  2. The size of the nucleus is of the order of 10-10 cm.
  3. The mass of the atom is concentrated in the “point” nucleus at the center.
  4. The volume of the atom is made up of electrons.
  5. Electrons are in a dynamic equilibrium in a plane around the nucleus.
  6. The nucleus of the atom is positively charged, while the electrons are negatively charged.
  7. The total negative charge of the electrons is equal to the positive charge of the nucleus.
  8. Electrons are in a state of perpetual motion within the atom (like the atoms are in a fluid).
  9. It takes energy to push the electron closer to the nucleus.
  10. A chemical element can have different atomic weights.



  1. The bound electron within the atom is same as the individual unbound electron outside the atom.
  2. Mass of the electron is negligibly small in comparison with that of the nucleus.
  3. The velocity of the electron is small compared to that of light.
  4. Electron, settled in a circular, stationary orbit around the nucleus, can be treated by ordinary mechanics.
  5. Passing of the systems between different stationary states cannot be treated by ordinary mechanics, but by emission of a homogenous radiation, per Planck’s theory.
  6. During the binding of the electron a homogenous radiation is emitted (equal to half the frequency of revolution of the electron in its final orbit).


The World of Atom (Part VIII)

ReferenceA Logical Approach to Theoretical Physics



Chapter 41: The Discovery of Cosmic Rays – Viktor F. Hess (1883 – 1964)
Penetrating Radiation in Seven free Balloon Flights. When these very energetic particles strike the earth’s atmosphere, they give rise to vast showers of other atomic and subatomic particles.

Chapter 42: The Cloud Chamber – Charles Thomson Rees Wilson (1869 – 1959)
On an Expansion Apparatus for Making Visible the Tracks of Ionizing Particles in Gases and Some Results Obtained by Its Use. The marvel of seeing the path of charged atomic particles and of atomic collisions was realized through the trails of fog-like droplets that the particles left in their wakes.


Sub-atomic particles are essentially rays and not waves.


The World of Atom (Part VII)

ReferenceA Logical Approach to Theoretical Physics



Chapter 37: The “Thomson” Atom – J. J. Thomson (1856 – 1940)
An Arrangement of Corpuscles in the Atom. The electrons are assumed to be corpuscles because their charges are quantized.

Chapter 38: The Determination of Avogadro’s Number – Jean Perrin (1870 – 1942)
Brownian Motion and Molecular Reality. It suggests that every fluid is formed of elastic molecules, animated by a perpetual motion.

Chapter 39: The Alpha-Particle and Helium – Ernest Rutherford (1871 – 1937)
The Nature of the Alpha-Particle from Radioactive Substance. Direct proof that alpha-particles are indeed ionized helium atoms

Chapter 40: Atoms of Electricity – Robert Andrews Millikan (1868 – 1953)
The Atomic Nature of Electricity. Direct experimental measurements to show the constancy of charge and its value.


Unlike the material particles, the sub-atomic particles are fuzzy.