# Quantum Theory Research Paper

*Posted on*April 15, 2009

Quantum theory, the modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles, is one of the most important theories devised in the 20th century. The theory is revolutionary as it replaces classical physics in the description of events at the microscopic level and now the theory provides the foundation for modern physics and chemistry.

The person who formed the basis of the quantum theory was Max Planck. In the 19th century, scientists used laws of classical physics to explain the relationship between matter and energy. Toward the end of the 19th century, various experimental results were obtained that could not be explained by classical physics. One of the failures of classical physics was the inability to explain the observed frequency distribution of radiant energy emitted by a hot blackbody. Classical physics predicts that when a blackbody is heated, the frequencies of the light radiated will take on a continuous range of values from zero to infinity. However, from experimental observations, the frequency distribution reaches a maximum and then falls off to zero as the frequency increases. In 1900, Max Planck announced a theory to explain the observed frequency distribution of blackbody radiation. He suggested that a blackbody atom radiating light of frequency v is restricted to emitting an amount of energy given by hv (where h is the Planck’s constant). Planck called this definite amount of energy a quantum of energy. In classical physics, energy is a continuous variable. In quantum physics, energy is quantized, meaning that energy can take on only certain values.

After Planck announced his theory, Albert Einstein applied the concept of energy quantization to the explanation of the experimental observations in the photoelectric effect. The photoelectric effect is a phenomenon when electrons are ejected from a substance exposed to electromagnetic radiation. According to classical physics, the average energy carried by an ejected electron should increase with the intensity of the incident radiation and not the frequency. However, from experimental observations, the energy of electrons ejected depends on the frequency of the incident radiation. Increasing the intensity of the incident radiation would only increase the amount and not the average energy of the electrons ejected. Also, for every substance irradiated, there is a threshold frequency below which no electrons are ejected irrespective of the light intensity. In 1905, Einstein explained the photoelectric effect by extending Planck’s concept of energy quantization to electromagnetic radiation. He proposed that besides having wavelike properties, electromagnetic radiation can be considered to consist of individual quanta, called photons, which interact with the electrons in the substance like discrete particles. For a given frequency v of the incident radiation, each photon carries a definite amount of energy given by hv, where h is the Planck’s constant. The threshold frequency is explained by the different nature of the materials. For each material there is a certain minimum energy, called the work function F, necessary to liberate an electron. Thus the threshold frequency, v0, corresponds to a minimum energy packet, hv0 (=F), required to liberate the electron.

The next major contribution to the quantum theory was Niels Bohr’s model of the hydrogen atom. When hydrogen gas is heated, the hydrogen atoms emit electromagnetic radiation of only certain distinct frequencies. During 1885 to 1910, Rydberg and Balmer independently found an empirical formula, called the Rydberg equation, which correctly reproduces the observed hydrogen atom spectral frequencies. However, there was no explanation for this formula. Meanwhile, in 1911, Rutherford introduced his atomic model, a dense, positively charged nucleus surrounded by a revolving, negatively charged electron cloud. According to classical physics, Rutherford’s atom is unstable because the negative electrons are attracted by the positive nucleus. As a result, the electrons will spiral into the nucleus releasing huge amounts of energy and the electrons’ spectral frequencies will change continuously. In 1913, Bohr introduced his theory of the hydrogen atom by applying quantum theory to Rutherford’s electron cloud. In his theory, Bohr postulated that the electrons can only revolve about the nucleus in fixed orbits of different energy values, such that the angular momentum of the revolving electron are quantized. When an electron is in an allowed orbit, the atom does not radiate energy. Such an electron is said to be in the stationary state and it has a certain amount of energy. If the electron makes its transitions from one energy level to another, photons of energies corresponding to the difference between the initial and final energy levels are emitted or absorbed. This gives rise to the set of characteristic line spectra and the Rydberg equation can finally be explained.

After Bohr announced his theory of the hydrogen atom, attempts were made to apply Bohr’s theory to atoms with more than one electron and to molecules. However, all attempts to derive the spectra of such systems using extensions of Bohr’s theory failed. A key idea towards resolving these difficulties was advanced by Louis de Broglie in 1923. He proposed that just as light shows both wave and particle like behaviours, matter also has a “dual” nature. He assumed that any particle, for example, an electron, an atom, etc, has a wavelength l which is given by h/p , where h is the Planck’s constant and p is the particles’ momentum. De Broglie obtained this equation by reasoning in analogy with photons. Although photons don’t have mass, but they do have energy. As Einstein famously proved, mass and energy are related in the equation E = mc2 where E is the energy, m is the mass and c is the speed of light. At speed c, a photon has a nonzero mass m. So by combining the 2 formulae, E = mc2 and E = hv , de Broglie obtained the equation l = h/p . In 1927, his hypothesis was experimentally confirmed by Davisson and Germer, who observed diffraction effects when an electron beam was reflected from a crystal of nickel. Since then, similar diffraction effects have been observed with neutrons, protons, helium atoms, and hydrogen molecules, indicating that the de Broglie hypothesis applies to all material particles, not just electrons.

After the 1920s, more and more observations were found to prove the validity of the quantum theory. Soon, the quantum theory led to the modern theory of the interaction between matter and radiation known as quantum mechanics, which generalized and replaced classical mechanics and Maxwell’s electromagnetic theory. Since then, science never looked back, as the quest for the understanding of how everything works continued…

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