Radiation quantum mechanics

The results of the theory of quantum mechanics require that nuclear states have discrete energies. This is in contrast to classical mechanical systems, which can have any of a continuous range of energies. This difference is a critical fact in the appHcations of radioactivity measurements, where the specific energies of radiations are generally used to identify the origin of the radiation. Quantum mechanics also shows that other quantities have only specific discrete values, and the whole understanding of atomic and nuclear systems depends on these discrete quantities. 

But occurrence of a chemical reaction along one or even several mean free paths is quite surprising, and to explain such a large reaction rate and large velocity of propagation, these authors resorted to electrons and radiation, quantum-mechanical resonance of collectively moving particles and direct impact of rapid active centers of a chain reaction. 

In the case of NMR spectroscopy we will be concerned only with absorption and emission of rf radiation. Quantum mechanics, the field of physics that deals with energy at the microscopic (atomic) level, allows us to define selection rules that describe the probability for a photon to be absorbed or emitted under a given set of circumstances. But even classical (i.e., pre-quantum-mechanical) physics tells us there is one requirement shared by all forms of absorption and emission spectroscopy For a particle to absorb (or emit) a photon, the particle itself must first be in some sort of uniform periodic motion with a characteristic fixed frequency. Most important, the frequency of that motion must exactly match the frequency of the absorbed (or emitted) photon ... 

We now consider the interaction of an atom or molecule with electromagnetic radiation. A proper quantum-mechanical approach would treat both the atom and the radiation quantum mechanically, but we shall simplify things by using the classical picture of the light as an electromagnetic wave of oscUlating electric and magnetic fields. 

Planck, Max (1858-1947) A German theoretical physicist credited with foimding quantum theory— which affects all matter in the universe—Planck earned a doctoral degree at the age of twenty-one before becoming a professor at the imiversities of Kiel and Berlin. He explored electromagnetic radiation, quantum mechanics, thermodynamics, black-bodies, and entropy. He formulated the Planck constant, which describes the proportions between the energy and frequency of a photon and provides understanding of atomic strucmre. He was awarded the 1918 Nobel Prize in Physics for his discoveries. 

The first illustrative problem comes from quantum mechanics. An equation in radiation density can be set up but not solved by conventional means. We shall guess a solution, substitute it into the equation, and apply a test to see whether the guess was right. Of course it isn t on the first try, but a second guess can be made and tested to see whether it is closer to the solution than the first. An iterative routine can be set up to cany out very many guesses in a methodical way until the test indicates that the solution has been approximated within some narrow limit. 

Several questions present themselves immediately How good does the initial guess have to be How do we know that the procedure leads to better guesses, not worse How many steps (how long) will the procedure take How do we know when to stop These questions and others like them will play an important role in this book. You will not be surprised to leam that answers to questions like these vary from one problem to another and cannot be set down once and for all. Let us start with a famous problem in quantum mechanics blackbody radiation. 

In principle, emission spectroscopy can be applied to both atoms and molecules. Molecular infrared emission, or blackbody radiation played an important role in the early development of quantum mechanics and has been used for the analysis of hot gases generated by flames and rocket exhausts. Although the availability of FT-IR instrumentation extended the application of IR emission spectroscopy to a wider array of samples, its applications remain limited. For this reason IR emission is not considered further in this text. Molecular UV/Vis emission spectroscopy is of little importance since the thermal energies needed for excitation generally result in the sample s decomposition. 

In 1913 Niels Bohr proposed a system of rules that defined a specific set of discrete orbits for the electrons of an atom with a given atomic number. These rules required the electrons to exist only in these orbits, so that they did not radiate energy continuously as in classical electromagnetism. This model was extended first by Sommerfeld and then by Goudsmit and Uhlenbeck. In 1925 Heisenberg, and in 1926 Schrn dinger, proposed a matrix or wave mechanics theory that has developed into quantum mechanics, in which all of these properties are included. In this theory the state of the electron is described by a wave function from which the electron s properties can be deduced. 

Quantum Mechanics has been the most spectacularly successful theory in the history of science. As is often mentioned the accuracy to which the anomalous magnetic moment of the electron can be calculated is a staggering nine decimal places. Quantum Mechanics has revolutionized the study of radiation and matter since its inception just over one hundred years ago. The impact of the theoiy has been felt in... 

The quantum mechanical view of Raman scatering sees a radiation field hvo inducing a transition from a lower level A to a level n. If vnlc is the transition frequency, then the inelastically scattered light has frequency v0 — v t. That is, the molecule removes energy hv k from an incident photon. This process corresponds to Stokes scattering. Alternatively, a molecule under-... 

One aspect of the mathematical treatment of the quantum mechanical theory is of particular interest. The wavefunction of the perturbed molecule (i.e. the molecule after the radiation is switched on ) involves a summation over all the stationary states of the unperturbed molecule (i.e. the molecule before the radiation is switched on ). The expression for intensity of the line arising from the transition k —> n involves a product of transition moments, MkrMrn, where r is any one of the stationary states and is often referred to as the third common level in the scattering act. 

The third common level is often invoked in simplified interpretations of the quantum mechanical theory. In this simplified interpretation, the Raman spectrum is seen as a photon absorption-photon emission process. A molecule in a lower level k absorbs a photon of incident radiation and undergoes a transition to the third common level r. The molecules in r return instantaneously to a lower level n emitting light of frequency differing from the laser frequency by —>< . This is the frequency for the Stokes process. The frequency for the anti-Stokes process would be + < . As the population of an upper level n is less than level k the intensity of the Stokes lines would be expected to be greater than the intensity of the anti-Stokes lines. This approach is inconsistent with the quantum mechanical treatment in which the third common level is introduced as a mathematical expedient and is not involved directly in the scattering process (9). 

Historical Background.—Relativistic quantum mechanics had its beginning in 1900 with Planck s formulation of the law of black body radiation. Perhaps its inception should be attributed more accurately to Einstein (1905) who ascribed to electromagnetic radiation a corpuscular character the photons. He endowed the photons with an energy and momentum hv and hv/c, respectively, if the frequency of the radiation is v. These assignments of energy and momentum for these zero rest mass particles were consistent with the postulates of relativity. It is to be noted that zero rest mass particles can only be understood within the framework of relativistic dynamics. 

For studies in molecular physics, several characteristics of ultrafast laser pulses are of crucial importance. A fundamental consequence of the short duration of femtosecond laser pulses is that they are not truly monochromatic. This is usually considered one of the defining characteristics of laser radiation, but it is only true for laser radiation with pulse durations of a nanosecond (0.000 000 001s, or a million femtoseconds) or longer. Because the duration of a femtosecond pulse is so precisely known, the time-energy uncertainty principle of quantum mechanics imposes an inherent imprecision in its frequency, or colour. Femtosecond pulses must also be coherent, that is the peaks of the waves at different frequencies must come into periodic alignment to construct the overall pulse shape and intensity. The result is that femtosecond laser pulses are built from a range of frequencies the shorter the pulse, the greater the number of frequencies that it supports, and vice versa. 

Let us now consider how electromagnetic radiation can interact with a particle of matter. Quantum mechanics (the field of physics dealing with... 

When Planck used this relationship to calculate the spectrum of blackbody radiation, he came up with a result that agreed perfectly with experiment. More importantly, he had discovered quantum mechanics. Energy emitted by a blackbody is not continuous. Instead, it comes in tiny, irreducible packets or quanta (a word coined by Planck himself) that are proportional to the frequency of the oscillator that generated the radiation. 

The numerical combination of protons and neutrons in most nuclides is such that the nucleus is quantum mechanically stable and the atom is said to be stable, i.e., not radioactive however, if there are too few or too many neutrons, the nucleus is unstable and the atom is said to be radioactive. Unstable nuclides undergo radioactive transformation, a process in which a neutron or proton converts into the other and a beta particle is emitted, or else an alpha particle is emitted. Each type of decay is typically accompanied by the emission of gamma rays. These unstable atoms are called radionuclides their emissions are called ionizing radiation and the whole property is called radioactivity. Transformation or decay results in the formation of new nuclides some of which may themselves be radionuclides, while others are stable nuclides. This series of transformations is called the decay chain of the radionuclide. The first radionuclide in the chain is called the parent the subsequent products of the transformation are called progeny, daughters, or decay products. 

All the nucleic acid bases absorb UV radiation, as seen in Tables 11-1, 11-2, 11-3, 11-4, and 11-5, making them vulnerable to the UV radiation of sunlight, since the energy of the photons absorbed could lead to photochemical reactions. As already mentioned above, the excited state lifetimes of the natural nucleobases, and their nucleotides, and nucleosides are very short, indicating that ultrafast radiationless decay to the ground state takes place [6], The mechanism for nonradiative decay in all the nucleobases has been investigated with quantum mechanical methods. Below we summarize these studies for each base and make an effort to find common mechanisms if they exist. 

As for any quantum mechanical system interacting with electromagnetic radiation, a photon can induce either absorption or emission. The experiment detects net absorption, i.e., the difference between the number of photons absorbed and the number emitted. Since absorption is proportional to the number of spins in the lower level and emission is proportional to the number of spins in the upper level, net absorption, i.e., absorption intensity, is proportional to the difference ... 

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