Energy quantised

The energies of the various contributions are quantised , i.e., in a given state the isolated molecule may possess one of a discrete set of values these values are often referred to as energy levels. When a molecule absorbs light, its energy is momentarily increased by an amount equal to that of the photon. The energy is related to the wave length (X) and frequency (v) by the equation ... 

When Max Planck wrote his remarkable paper of 1901, and introduced what Stehle (1994) calls his time bomb of an equation, e = / v , it took a number of years before anyone seriously paid attention to the revolutionary concept of the quantisation of energy the response was as sluggish as that, a few years later, whieh greeted X-ray diffraction from crystals. It was not until Einstein, in 1905, used Planck s concepts to interpret the photoelectric effect (the work for which Einstein was actually awarded his Nobel Prize) that physicists began to sit up and take notice. Niels Bohr s thesis of 1911 which introduced the concept of the quantisation of electronic energy levels in the free atom, though in a purely empirical manner, did not consider the behaviour of atoms assembled in solids. 

Transitions between two quantised energy levels, say from E0 to , correspond to the absorption of radiant energy, and the amount of energy absorbed (AE) is determined by Bohr s equation... 

The Stefan-Boltzmann Law and Wien s Law for black body radiation have been unified into Planck s Law for black body radiation, from which Planck s constant was first introduced. Planck s analysis of the spectral distribution of black body radiation led him to an understanding of the quantisation of energy and radiation and the role of the photon in the theory of radiation. The precise law relates the intensity of the radiation at all wavelengths with the temperature and has the form ... 

Unfortunately, the Schrodinger equation for multi-electron atoms and, for that matter, all molecules cannot be solved exactly and does not lead to an analogous expression to Equation 4.5 for the quantised energy levels. Even for simple atoms such as sodium the number of interactions between the particles increases rapidly. Sodium contains 11 electrons and so the correct quantum mechanical description of the atom has to include 11 nucleus-electron interactions, 55 electron-electron repulsion interactions and the correct description of the kinetic energy of the nucleus and the electrons - a further 12 terms in the Hamiltonian. The analysis of many-electron atomic spectra is complicated and beyond the scope of this book, but it was one such analysis performed by Sir Norman Lockyer that led to the discovery of helium on the Sun before it was discovered on the Earth. 

Ultraviolet absorption spectra appear when outer electrons of atoms or molecules absorb radiant energy and undergo transition to higher energy levels. These transitions are quantised and depends on the compound under examination. 

Understand the concept of the quantised nature of light and matter and be able to draw simple diagrams showing quantised energy levels in atoms and molecules. 

The development of the quantum theory in the early twentieth century allowed predictions to be made relating to the properties and behaviour of matter and light. The electrons in matter have both wavelike and particle-like properties, and quantum theory shows that the energy of matter is quantised that is, only certain specific energies are allowed. 

The quantised energy levels of matter have a separation that is of the same order as the energy of visible or ultraviolet light. Thus the absorption of visible or ultraviolet light by matter can excite electrons to higher energy levels, producing electronically-excited species. 

Figure 1.1 Quantised energy levels in matter, where an electron ( ) may be found in either of the two energy levels shown...

According to the quantum theory, light is also quantised. The absorption or emission of light occurs by the transfer of energy as photons. These photons have both wavelike and particle-like properties and each photon has a specific energy, E, given by Planck s law ... 

There are three basic processes of light-matter interaction that can induce transfer of an electron between two quantised energy states ... 

Erwin Schrodinger developed an equation to describe the electron in the hydrogen atom as having both wavelike and particle-like behaviour. Solution of the Schrodinger wave equation by application of the so-called quantum mechanics or wave mechanics shows that electronic energy levels within atoms are quantised that is, only certain specific electronic energy levels are allowed. 

Some aspects of the bonding in molecules are explained by a model called molecular orbital theory. In an analogous manner to that used for atomic orbitals, the quantum mechanical model applied to molecules allows only certain energy states of an electron to exist. These quantised energy states are described by using specific wavefunctions called molecular orbitals. 

Figure 1.7 shows a simple representation of the relative quantised energy levels found in organic molecules. 

The energy gap between electronic states is much greater than that between vibrational states, which in turn is much greater than that between rotational states. As a result, we are able to adequately describe the effects of electronic transitions within molecules by considering quantised electronic and vibrational states. 

Figure 2.2 Schematic diagram of the electronic ground state and the first excited electronic state, with their associated quantised vibrational energy levels, for an organic molecule. The vertical arrows show vibronic transitions due to the absorption of photons...

Figure 2.3 A Morse curve for a diatomic molecule, showing the quantised vibrational energy levels. The minimum on the curve represents the equilibrium bond distance, re...

Each line in an atomic emission spectrum corresponds to the energy given out when an excited electron moves to a state of lower energy. This can either be to a lower excited state or back to the ground state. Atomic emission spectra provide good evidence for discrete (quantised) energy levels in atoms. 

Electrons within atoms are said to be quantised. This means that they can only possess fixed amounts of energy known as quanta. As a result, electrons can be defined in terms of quantum numbers. 

Spectroscopy is the study of the quantised interaction of energy (typically electromagnetic energy) with matter. In Organic Chemistry, we typically deal with molecular spectroscopy i.e. the spectroscopy of atoms that are bound together in molecules. 

A spectrum consists of distinct bands or transitions because the absorption (or emission) of energy is quantised. The energy gap of a transition is a molecular property and is characteristic of molecular structure. 

Band emissions, on the other hand, are characteristic of excited molecules and a molecule, like an atom, can exist in a number of electronic energy levels. The change from one particular level to another results from the absorption or emission of a definite i.e. quantised) amount of energy. But, because of simultaneous changes which occur in the rotational or vibrational energy of the molecule, a series of closely spaced lines appear in the spectrum in the form of a band. 

The energy is thus quantised, with quantum number a... 

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