File Name: measurement and instrumentation quastion and answer stasics and daynamics caracterstics signal .zip
Student's Solutions Guide. Since the textbook's initial publication, many requested the distribution of solutions to the problems in the textbook. Probability, Statistics, and Random Processes for Electrical Engineering a Histograms for a Gaussian random variable for and samples.
Measuring Vibration: The Complete Guide
Fluorescence and phosphorescence are types of molecular luminescence methods. A molecule of analyte absorbs a photon and excites a species. The emission spectrum can provide qualitative and quantitative analysis.
The term fluorescence and phosphorescence are usually referred as photoluminescence because both are alike in excitation brought by absorption of a photon. In phosphorescence, there is a change in electron spin, which results in a longer lifetime of the excited state second to minutes.
Fluorescence and phosphorescence occurs at longer wavelength than the excitation radiation. Fluorescence can occur in gaseous, liquid, and solid chemical systems.
The simple kind of fluorescence is by dilute atomic vapors. A fluorescence example would be if a 3s electron of a vaporized sodium atom is excited to the 3p state by absorption of a radiation at wavelength After 10 -8 s, the electron returns to ground state and on its return it emits radiation of the two wavelengths in all directions. This type of fluorescence in which the absorbed radiation is remitted without a change in frequency is known as resonance fluorescence. Resonance fluorescence can also occur in molecular species.
Molecular fluorescence band centers at wavelengths longer than resonance lines. The shift toward longer wavelength is referred to as the Stokes Shift. Understanding the difference between fluorescence and phosphorescence requires the knowledge of electron spin and the differences between singlet and triplet states.
These opposite spin states are called spin pairing. Because of this spin pairing, most molecules do not exhibit a magnetic field and are diamagnetic. In diamagnetic molecules, electrons are not attracted or repelled by the static electric field. Free radicals are paramagnetic because they contain unpaired electrons have magnetic moments that are attracted to the magnetic field.
Singlet state is defined when all the electron spins are paired in the molecular electronic state and the electronic energy levels do not split when the molecule is exposed into a magnetic field. A doublet state occurs when there is an unpaired electron that gives two possible orientations when exposed in a magnetic field and imparts different energy to the system. A singlet or a triplet can form when one electron is excited to a higher energy level.
In an excited singlet state, the electron is promoted in the same spin orientation as it was in the ground state paired. In a triplet excited stated, the electron that is promoted has the same spin orientation parallel to the other unpaired electron. The difference between a molecule in the ground and excited state is that the electrons is diamagnetic in the ground state and paramagnetic in the triplet state.
This difference in spin state makes the transition from singlet to triplet or triplet to singlet more improbable than the singlet-to-singlet transitions.
This singlet to triplet or reverse transition involves a change in electronic state. For this reason, the lifetime of the triplet state is longer the singlet state by approximately 10 4 seconds fold difference. The radiation that induced the transition from ground to excited triplet state has a low probability of occurring, thus their absorption bands are less intense than singlet-singlet state absorption. The excited triplet state can be populated from the excited singlet state of certain molecules which results in phosphorescence.
These spin multiplicities in ground and excited states can be used to explain transition in photoluminescence molecules by the Jablonski diagram. The Jablonski diagram that drawn below is a partial energy diagram that represents the energy of photoluminescent molecule in its different energy states. At room temperature, majority of the molecules in a solution are in this state. The upper lines represent the energy state of the three excited electronic states: S 1 and S 2 represent the electronic singlet state left and T 1 represents the first electronic triplet state right.
The upper darkest line represents the ground vibrational state of the three excited electronic state. The energy of the triplet state is lower than the energy of the corresponding singlet state. There are numerous vibrational levels that can be associated with each electronic state as denoted by the thinner lines. This transition leads to a change in multiplicity and thus has a low probability of occurring which is a forbidden transition.
The knowledge of forbidden transition is used to explain and compare the peaks of absorption and emission. The table below compares the absorption and emission rates of fluorescence and phosphorescence. The rate of photon absorption is very rapid. Fluorescence emission occurs at a slower rate. Since the triplet to singlet or reverse is a forbidden transition, meaning it is less likely to occur than the singlet-to-singlet transition, the rate of triplet to singlet is typically slower.
Therefore, phosphorescence emission requires more time than fluorescence. The favored deactivation process is the route that is most rapid and spends less time in the excited state. If the rate constant for fluorescence is more favorable in the radiationless path, the fluorescence will be less intense or absent.
After discussing all the possible deactivation processes, variable that affect the emissions to occur. Molecular structure and its chemical environment influence whether a substance will fluoresce and the intensities of these emissions. The quantum yield or quantum efficiency is used to measure the probability that a molecule will fluoresce or phosphoresce.
For fluorescence and phosphorescence is the ratio of the number of molecules that luminescent to the total number of excited molecules. For highly fluoresce molecules, the quantum efficiency approaches to one. Molecules that do not fluoresce have quantum efficiencies that approach to zero. They are related by the quantum yield equation given below:. The magnitudes of kf , kd, and kpd depend on the chemical structure, while the rest of the constants ki, kec, and kic are strongly influenced by the environment.
Fluorescence rarely results from absorption of ultraviolet radiation of wavelength shorter than nm because radiation at this wavelength has sufficient energy to deactivate the electron in the excited state by predissociation or dissociation. Molecules that are excited electronically will return to the lowest excited state by rapid vibrational relaxation and internal conversion, which produces no radiation emission.
Fluorescence arises from a transition from the lowest vibrational level of the first excited electronic state to one of the vibrational levels in the electronic ground state. A few aliphatic, alicyclic carbonyl, and highly conjugated double-bond structures also exhibit fluorescence as well. Most unsubstituted aromatic hydrocarbons fluoresce in solution too. The quantum efficiency increases as the number of rings and the degree of condensation increases. Simple heterocycles such as the structures listed below do not exhibit fluorescence.
Although simple heterocyclics do not fluoresce, fused-ring structures do. For instance, a fusion of a benzene ring to a hetercyclic structure results in an increase in molar absorptivity of the absorption band.
The lifetime of the excited state in fused structure and fluorescence is observed. Examples of fluorescent compounds is shown below. Benzene ring substitution causes a shift in the absorption maxima of the wavelength and changes in fluorescence emission. The table below is used to demonstrate and visually show that as benzene is substituted with increasing methyl addition, the relative intensity of fluorescence increases. The relative intensity of fluorescence increases as oxygenated species increases in substitution.
The values for such increase is demonstrated in the table below. Influence of a halogen substitution decreases fluorescence as the molar mass of the halogen increases. As demonstrated in the table below, as the molar mass of the substituted compound increases, the relative intensity of the fluorescence decreases.
In heavy atom substitution such as nitro derivatives or heavy halogen substitution such as iodobenzene, the compounds are subject to predissociation. These compounds have bonds that easily rupture that can then absorb excitation energy and go through internal conversion.
Therefore, the relative intensity of fluorescence and fluorescent wavelength is not observed and this is demonstrated in the table below. Fluorescence is particularly favored in molecules with rigid structures. The table below compares the quantum efficiencies of fluorine and biphenyl which are both similar in structure that there is a bond between the two benzene group.
The difference is that fluorene is more rigid from the addition methylene bridging group. By looking at the table below, rigid fluorene has a higher quantum efficiency than unrigid biphenyl which indicates that fluorescence is favored in rigid molecules. This concept of rigidity was used to explain the increase in fluorescence of organic chelating agent when the compound is complexed with a metal ion. The fluorescence intensity of 8-hydroxyquinoline is much less than its zinc complex.
The explanation for lower quantum efficiency or lack of rigidity in caused by the enhanced internal conversion rate k ic which increases the probability that there will be radiationless deactivation. Nonrigid molecules can also undergo low-frequency vibration which accounts for small energy loss.
Quantum efficiency of Fluorescence decreases with increasing temperature. As the temperature increases, the frequency of the collision increases which increases the probability of deactivation by external conversion. Solvents with lower viscosity have higher possibility of deactivation by external conversion. Fluorescence of a molecule decreases when its solvent contains heavy atoms such as carbon tetrabromide and ethyl iodide, or when heavy atoms are substituted into the fluorescing compound.
Orbital spin interaction result from an increase in the rate of triplet formation, which decreases the possibility of fluorescence. Heavy atoms are usually incorporated into solvent to enhance phosphorescence. The fluorescence of aromatic compound with basic or acid substituent rings are usually pH dependent. The wavelength and emission intensity is different for protonated and unprotonated forms of the compound as illustrated in the table below:.
The emission changes of this compound arises from different number of resonance structures associated with the acidic and basic forms of the molecule. The additional resonance forms provides a more stable first excited state, thus leading to fluorescence in the ultraviolet region. The resonance structures of basic aniline and acidic anilinium ion is shown below:.
An example of this type of fluorescence seen in compound as a function of pH is the phenolic form of 1-naphtholsulfonic acid. This compound is not detectable with the eye because it occurs in the ultraviolet region, but with an addition of a base, it becomes converted to a phenolate ion, the emission band shifts to the visible wavelength where it can be visually seen.
Acid dissociation constant for excited molecules differs for the same species in the ground state. These changes in acid or base dissociation constant differ in four or five orders of magnitude.
Dissolved oxygen reduces the intensity of fluorescence in solution, which results from a photochemically induced oxidation of fluorescing species. Quenching takes place from the paramagnetic properties of molecular oxygen that promotes intersystem crossing and conversion of excited molecules to triplet state.
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Fluorescence and phosphorescence are types of molecular luminescence methods. A molecule of analyte absorbs a photon and excites a species. The emission spectrum can provide qualitative and quantitative analysis. The term fluorescence and phosphorescence are usually referred as photoluminescence because both are alike in excitation brought by absorption of a photon. In phosphorescence, there is a change in electron spin, which results in a longer lifetime of the excited state second to minutes. Fluorescence and phosphorescence occurs at longer wavelength than the excitation radiation. Fluorescence can occur in gaseous, liquid, and solid chemical systems.
As vibration isolation and reduction techniques have become an integral part of machine design, the need for accurate measurement and analysis of mechanical vibration has grown. Using accelerometers to convert vibratory motion into an electrical signal, the process of measurement and analysis is ably performed by the versatile abilities of modern electronics. A body is said to vibrate when it describes an oscillating motion about a reference position. The number of times a complete motion cycle takes place during the period of a second is called the frequency and is measured in hertz Hz. The motion can consist of a single component occurring at a single frequency, as with a tuning fork, or of several components occurring at different frequencies simultaneously, for example, with the piston motion of an internal combustion engine.
How to use measurement in a sentence. There are worksheets for linear measurement with a ruler - yards, feet, inches. Bioenergy Laboratory. Mechanical Engineering - The degree of reproducibility among several independent measurements of the same true value under reference conditions.
The application bit-true simu-lation and the real execution give identical results at the bit level. With this mathematical analysis as a background, let us move on to obtaining the results from quick MATLAB simulations with levels. Download Now.
The performance of any measuring instrument is affected by several factors. There are two basic performance characteristics of measuring instruments. Static Characteristics and Dynamic Characteristics. Static Characteristics:. Static Error : The difference between the true value of the measuring quantity to the value shown by the measuring instrument under not varying process conditions. The measured quantity may be different from the true value due to the effects of temperature, humidity, etc. It composed of two characteristics: conformity and significant figures.
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