The discovery of the photoelectric effect in 1902, which unequivocally established the dual nature of light, led to the realization of the dual nature of particles as well. This revolutionary insight into the behavior of particles, although it fetched a 1924 Nobel Prize in Physics to Louis de Broglie, dragged physics into rough weather. It is common knowledge that waves, when bounded by a constraint, can exist only at discrete frequencies or wavelengths. For example, in the case of a rope, rigidly clamped at the two ends, only waves, half of whose wavelength times an integer equals the rope’s length, can be impressed upon it. Ascription of the wave nature to a particle, therefore, means that if the particle is confined within a region in space, the wavelengths that fit into this space will only be allowed. As the energy of a particle is linked to its wavelength, this restriction on wavelength, in turn, restricts the values of energy that the particle can possess. The very concept of discretization of energy states of a particle seemed to have flummoxed the physics community in the early part of the twentieth century. After all, quantization of energy of a particle would be analogous to having only certain specific speeds at which a car can travel, a soccer ball can be kicked, or a baseball can be struck! This chapter explains why energy quantization has no observable bearing in the world we live in but controls the behavior of microscopic particles that constitute the quantum world. It also will enlighten its readers as to how the energy quantization manifests into the spectral emission from atoms, molecules, or ions, the gateway leading to the realization of lasers.

1. 1.

   A continuous sequence in which the adjacent energy levels are not perceptibly different from each other

2. 2.

   Centripetal force acts on a body that performs a curved motion and is directed toward the center of rotation. In case of planetary motion, the gravitational attraction between the Sun and the planet provides the centripetal force. If you tie an object to one end of a rope and rotate it by holding the other end, the tension developed in the taut rope supplies the centripetal force necessary to keep it moving. Centripetal force in case of a particle of massm rotating at a velocity\( v \) in a circular path of radiusr is given by\( \frac{m{v}^2}{r} \).

3. 3.

   Potential energy of the electron here is negative as it is being electrically attracted by the proton and equals the work required to be imparted in order to move the electron through a distance between r_n to infinity.

4. 4.

   eV is normally the unit used to express the energy of atomic particles and 1 eV is equivalent to 1.6 × 10⁻¹⁹ J.

5. 5.

   Boltzmann chose to die by his own hand on September 5, 1906, when he was holidaying with his wife and daughter at a place close to the Italian town of Trieste. His suicide is blamed to a severe depression, he was suffering from, that stemmed basically from the strong opposition to his work on theorizing the population distribution. The irony is only a few weeks following this tragedy, his theory was experimentally verified. The suicide most certainly also drew a curtain on his getting a Nobel Prize that, incidentally, is not awarded posthumously.

Authors and Affiliations

1. Former Head, Laser and Plasma Technology Division, Bhabha Atomic Research Centre, Mumbai, India

   Dhruba J. Biswas

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