The position of an atom or the momentum of an electron can be observable by projecting the wave function onto an eigenstate. However, this projection only reveals a portion of the wave function and may destroy quantum features, such as superposition and entanglement. Until now, the matter was to find a tool that directly magnifies the microscopic state of a quantum particle onto the laboratory scale.

Aneta Stodolna and her colleagues demonstrated how photo-ionization microscopy directly maps out the nodal structure of an electronic orbital of a hydrogen atom placed in a electrical field. This tool allows to observe atomic system that has an analytical solution to the Schrondinger equation. The researchers utilized an electrostatic lens that magnifies the outgoing electron wave without disrupting its quantum coherence. They showed that interference pattern matches the nodal features of the hydrogen wave function which also can be calculated.

Figure 1Figure 1.

In these photo-ionization studies, researchers manipulated the molecules using static fields to induce a dipole. However, this was challenging because atoms don’t have external degrees of freedom. This was overcome by applying electrical field that defines a quantization axis in hydrogen and aligns the orbitals. This allowed to observe direct transverse orbital state, which is the projection of the orbital onto the plane perpendicular to the electric field.

Going off from here, Stodolna and her researchers started with a beam of hydrogen atoms that they exposed to a transverse laser. This moved the population of atoms from the ground state to the 2s and 2p orbitals. The second pulse moved the electron into a highly excited Rydberg state. Tuning the wavelength of the excited pulse can control the quantum numbers of the state and thereby manipulate the number of nodes in the wave  function. It was tuned to the state with n, principal quantum number, equal to 30. As you could see in the figure 1, The electron cannot exit against the dc electrical field, but can freely move in any other direction. The portion of the electron wave directed toward the 2D detector which interferes with the portion directed away from the detector. This produced an interference pattern on the detector and that the number of nodes in the detected interference pattern reproduced the nodal structure. This evidenced that the photo-ionization microscope provided the ability to directly visualize quantum orbital features.

The author of this article is Christopher T.L. Smeenk, and he is a postdoctoral researcher in the Department of Physics at University of Ottawa and Joint Attosecond Science Lab at National Research Council in Ottawa, Canada. Therefore, he must understand how this research works and know what he is writing about. In addition, this research article was published on May 2013 which is less than an year ago, so it can be considered as fairly updated information. The website that this article was published is American Physical Society, which is highly reliable as much as American Chemical Society.

In chapter 9, we learned about application of schrodinger’s equation to hydrogen atom and this research seemed show how to get to wave function through actual hands-on research that can be calculated using the Schrodinger’s equation. Also, this article talked about excitation of atom to other orbital states and in this chapter, we also talked about different quantum numbers and the wave functions associated with them.

Reference: https://physics.aps.org/articles/v6/58

2013_018_Nature_-_Kleinster_Schwingssensor_der_Quantenwelt72dpi The spin of a molecule (orange) changes and deforms the nanotube (black) mounted between two electrodes (gold). (Figure: C. Grupe/KIT)

Researchers of Karlsruhe Institute of Technology found basis of vibration sensors and quantum computers using magnetic spin of a molecule and carbon nanotubes. These are now considered building blocks of future nanoelectronic systems. In their research, carbon nanotube, that can vibrate mechanically, was mounted between two metal electrodes and spanned a distance of 1 micrometer. Then, they applied an organic molecule with incorporated metal atom so that molecule can spin. In the carbon nanotube, molecules can flip spins in parallel or anti-parallel direction to the magnetic field. As the spinning changes, the resulting recoil is transferred to the carbon nanotube and the latter starts to vibrate. The vibration changes the atomic distance and can be used as a measure of motion. The discovery of interaction between a magnetic spin and mechanical vibration can be used to determine the masses of individual molecules and further more, in quantum computers. For more information on this research find DOI: 10.1038/nano.2012.258

There are not much of class materials that I can relate to this research other than what is quantum mechanical vibration? In chapter 7 lecture, we talked about solving the Schrodinger equation of vibrational motion. This motion also can be called as harmonic oscillator and it is a motion where two masses are connected by a spring which can “stretch” to negative infinity to positive infinity. This type of motion both contains kinetic energy and potential energy. The wavefunction and the eigenvalue energy are dependent on the energy level. The lowest energy level it can get to is 0. We also learned that, like in research, the mass of desired molecule can be found using the expression for energy which is E = (v+1/2)hbarω. Here, v indicates the energy level, vibrational quantum number, hbar indicates plank constant over 2pi and the ω, omega, indicates (force constant, k/mass, m)^(1/2).

Karlsruhe Institute of Technology (KIT) is a public corporation to fulfill the mission of a national research center of the Helmholtz Association. They mainly focus on energy, nature, and the environment. This research article was published on actual KIT website on August 1st, 2013 which shows that this source is reliable. This website do not have much material to use as study supplement but, can learn about research occurring in Europe.

Reference: http://www.kit.edu/kit/english/pi_2013_12574.php

In chapter 4, we learned about application of Schrodinger equation, HΨ=EΨ on translational motion. This Schrodinger equation contains H, Hamiltonian operator, Ψ, psi, the wave function or an eigenfunction, E, Energy or an eigenvalue. This equation is very interesting because it is not an algebraic equation, meaning that two psi’s cannot be canceled out by dividing. This equation physically defines all of dynamical properties of a system. The wave function represents the system and the energy measures the properties.

Specifically, the wave function takes an important role in quantum mechanics. It contains all the information about the system, it can obtain probability information, can be normalized, and used in schrodinger equation as an eigenfunction.

Michael Byrne, the author, reported on Motherboard that a group of physicists in Brown University has succeeded in shattering a wave function. A wave function is a space occupied simultaneously by many different possibilities. Therefore, shattered wave function shows that unmeasured particle is able to occupy many states simultaneously, dissected into many parts.

Physicists found that it is possible to isolate the wave function into different parts. Let say, the particle has probability of being in position (x1,y2,z3) and another probability at (x2, y2, z2), these two probabilities can be isolated from each other. This experiment was achieved using a small helium bubbles as traps. One of physicist stated that, “We are trapping the chance of finding the electron, not pieces of the particle.”

This research dates back to the 1960’s. Back then, physicists observed behavior of electrons in supercooled baths of helium. When an electron entered the bath, it acted to repel the surrounding helium atoms and formed its own bubble. Then, this bubble will drop downward towards the detector on the bottom of the bath. However, before the bubble hits the detector, physicists found that there are “mystery” objects that arrives before the bubble and gets measured by the detector. Researchers argued that a fission reaction occurs and break the electron wave function apart into same sizes which are the “mystery” objects detected.

Since the wave function is not a physical thing, physicists are still unsure about what is actually contributing to the measurement.

Motherboard is a blog-type website that different field of researchers, scientists, writers can post articles about different science experiments and researchers that are happening around the U.S. and beyond. There are number of categories of Machines, Discoveries, Space, Futures, Culture and Earth and all of these sections offer to learn about science experiments that we can’t really observe in our daily life. This website also can be viewed in different languages indicating that it is published internationally too. The last update is 2015 which shows that all the information provided in this website is very recent.

 

Reference: http://motherboard.vice.com/read/how-could-quantum-physics-get-weirder-shattered-wavefunctions

The theory of Schrödinger’s cat states is the cat really alive and dead? (For more information about Schrodinger’s cat, go to https://www.youtube.com/watch?feature=player_embedded&v=IOYyCHGWJq4) Researchers at the University of Queensland attempted to answer this question using 4D states of photons. They states that describing the cat as dead and alive is due to lakcing real state. In their research, they let the cat to be the quantum wavefunction because Dr. Fedrizzi from the UQ School of Mathematics and Physics  said that quantum wavefunction is main tool in quantum mechanics but we are still not sure what it actually is. Their results showed that “if there is objective reality, the wavefunction corresponds to this reality.” This means that Schrodinger’s cat really is in a state of being both alive and dead.

Reference: http://www.uq.edu.au/news/article/2015/02/quantum-reality-check

I also found another research done by physicists at the University of Sussex that they developed a special Schrodinger’s cat using a new technology that based on trapped ions, also known as charged atoms, and microwave radiation. In their research, ions exist in two states simultaneously like the cat. Usually, lasers were used to drive quantum processes but, it would be very difficult to stabilize millions of beams. So, they built a quantum computer that uses microwave radiation because this type of radiation is early broadcast over a large area. Their research of controlling a Schrodinger’s cat ion using microwave radiation will give significant step up of technologies in quantum mechanics.

Reference: http://www.uq.edu.au/news/article/2015/02/quantum-reality-check

In class, we learned that Schrodinger’s equation is not an algebraic equation, where wavefunction cannot be divided by on both side, like the cat in the box that is considered both alive and dead. Also, the concepts of eigenfunction that function need to be exactly same before and after the operation. It is important to note how the Shrodinger’s equation was applied to Schrodinger’s cat and from there, we are now in the process of developing new technology of quantum computers.

These two articles were published on their universities websites. Therefore, these articles should be highly reliable and accurate to learn about what is other side of world doing with quantum mechanics. These sources, however, does not seem valuable as a study guide to learn about concepts of quantum mechanics.

Reference: http://quosa.biz/support/customers/actavis/Watson%20Articles/Laura%20-%2005-13-2013/Q9730605.pdf

Foods are composed of chemical and biochemical compounds that are responsible for flavor, texture, and nutritional value, as well as, harmful substances. All of these compounds are produced by chemical reactions. The most important chemical reactions in food are lipid oxidation, chain reactions of rancidity in oil and fat component, and non-enzymatic reactions of amines and reducing sugars. In these reactions, variables such as concentration, temperature, pH and water activity are considered in observing kinetic studies of food.

Quality is an attribute of food. Each food can be stored for certain amount of period under specific conditions. This period is called shelf-life. Kinetics such as enzymatic chemical, physical and microbial reactions are important aspects in food research to assess food quality and determine shelf-life. The rate of food quality change is expressed in function of composition and environmental factors.

dQ/dt=F(Ci,Ej)

The term Ci represents the composition factors, such as concentration of reactive compounds, inorganic catalysts, enzymes, reaction inhibitors, pH, water activity. The term Ej represents environmental factors such as temperature, relative humidity, total pressure and partial pressure of different gases, light and mechanical stresses.

Generally, in many food kinetics, the reactions are reversible in the form of aA+bB File:Equilibrium sign 15.pngcC +dD, with the rate constant of Kb. Therefore the reaction rate in this case would be

r=-d[A]/adt =-d[B]/bdt =+d[C]/cdt=+d[D]/ddt=kf[A]^a[B]^b-kb[C]^c[D]^d

In food degradation systems either kb is negligible compared to kf, or they are distant from equilibrium because [C] and [D] very small, which makes the reaction irreversible. In addition, the concentration of the reactant that primarily affects overall quality is limiting and the concentration of the other species are in large excess which cause the change in time to be negligible. Therefore, the quality loss rate equation is expressed in terms of specific reactants.

r=-d[A]/dt=k’f[A]^a

The quality of food can be determined by deriving zero, 1st, 2nd and even mth order reaction. From here, the half-life time of the reaction can be determined as well. The figure below is the graph of how quality of food can be determined using zeroth and first order reaction as the time goes.

Untitled

Temperature plays role in food kinetics because temperature and food quality have high correlation. Many of food kinetic model such as the shelf-life loss kinetic model based on environmental factors, such as temperature. The mostly used is the Arrhenius relation, derived from thermodynamic laws because many of food kinetic models follows an Arrhenius behavior with temperature.

There are many similarities between finding food quality and the chemical kinetics that we learned in class. Chemical kinetics measure the rate at which chemical reactions take place, and the reaction rate is dependent on the composition of the reaction mixture and temperature. These are important factors in determining the rate of food quality reaction. The rate law to express the quality of food is also written in terms of concentration and its stoichiometric coefficient. Then the integrated rate law and reaction orders can be used to find the percent of quality index. Also, shelf-life loss kinetic model mentioned above uses the temperature dependence reaction rates by applying the Arrhenius equation to assess how temperature affects the quality of the food.

This handbook for food engineering practice was published in 1997, so it is fairly old information. It might be old to use it for actual food engineering, but the physical chemistry aspects were very similar to what was presented in class. Therefore, I should say, this document is reliable. Names of authors are clearly stated, the year and the publishing company and etc.

In general, the Kinetic molecular theory of gases explains the behavior of gases. This theory connects the concepts of thermodynamics to kinetics; providing an explanation for development of the ideal gas law. The kinetic molecular theory is based on five assumptions: one, gas molecules are in constant random motion. Two, the volume of the molecule is negligible because the distance between gas molecules is greater than the size. Three, intermolecular interactions are negligible. Four, gas molecules collide with one of another, but they are elastic. Finally five, the average kinetic energy of the molecules are dependent on temperature and that all gaseous molecules have same kinetic energy at a given temperature.
From the website that I found, it talked about how the kinetic molecular theory of gases can explain the relationship among pressure, volume and temperature. First, at constant temperature, kinetic energy of a gas does not change. Similarly, when a gas is allowed to occupy a large volume, the kinetic energy of the molecules does not change (however, density and the average distance between molecules change). Therefore, when volume is large, the molecules collide with each other and the walls of their container less often which leads to a decrease in pressure. Second, increase in temperature will increase the average kinetic energy and the molecules will collide more often with greater force, which then will increase the pressure. Therefore, increase in temperature can be offset by increase in volume for the pressure to be unchanged in the container. Third, 3rd assumption of the kinetic molecular theory of gases stated that gas do not interact with one another. This concept leads to presence of one gas in a gas mixture having on effect on the pressure exerted by another which leads to the concept of Dalton’s law of partial pressures.
Website: http://catalog.flatworldknowledge.com/bookhub/4309?e=averill-chab
The website where I obtained my information seemed reliable to high extent because the two authors of this website, Bruce A. Averill who received his B.S. in Chemistry at Michigan State University and his Ph.D in inorganic chemistry at MIT in 1973. He won several recognition and named as a Jefferson Science Policy Fellow at the U.S. State Department. As well as, Patricia, Eldredge, who is other author for this website received her Ph.D in inorganic chemistry at Chapel Hill. She worked as analytical research chemist in industry. This webiste was created to be a supplement studying tool for chemistry students and this website was newly updated in 2014 which is very current. I definitely will use this website more often now on when I need to review my general chemistry concepts.

Electronic spectroscopy utilizes light absorption to change charge distribution of electrons about a molecule. The energy required for this change can often times lead to bond breakage. In electronic spectroscopy, diatomic molecules exist in the ground electronic state (lowest energy electronic state) at equilibrium. When the molecules are excited, the excitation results in changes in the vibrational level as well. Following the excitation, the molecule experiences a restoring force that brings it back down to the ground electronic state. The Franck-Condon principle states that transitions between electronic states can be described by the vertical line on an energy versus internuclear distance diagram. This principle operates under the premise that electrons respond much faster than the nucleus so changes in the nuclear geometry are not observed. The vertical transitions of electrons show that excitation from ground vibrational level does not necessarily go to the same vibrational level of the excited electronic state but can go to several different vibrational levels. The most intense line that is observed in an electronic spectrum arises from the transition whose wave functions of the ground vibrational level and the vibrational level of the excited electronic state overlap the most coherently. Once the electron is excited, it may relax non-radiatively followed by energy release as it returns to the ground state typically through fluorescence.

The link that I have posted above is a link to a video in which Dr. Ogilvie from the University of Michigan gives an overview of her research interest in understanding the design principles of photosynthetic systems in nature and then to extend that knowledge into making efficient synthetic light harvesting systems in hopes of tackling the world’s energy problem. She informs that photosynthetic systems consist of light absorbing pigments existing in reaction centers which help to harness solar energy and can do so using a wide range of the electromagnetic spectrum. The absorbed solar energy forms stable charge separations which drives photosynthesis later on. The tool that was used to study this behavior in photosystem II was 2 dimensional electronic spectroscopy. The video is rather fast because the target audience is probably people who are well versed in the subject at hand. An overview of the instrument that is used in the study is also shown. From 2-D spectra obtained at different time periods, the transfer time of the energy from an excited state to a lower state in photosystem II can be determined. Some background reading would be necessary to completely understand what is being presented. However, this does show a unique application of electronic spectroscopy in the real world to benefit society.

In regards to the credibility of the source, the video is associated with American Chemical Society and the people who appear in the video are linked with the Department of Physics and Biophysics at the University of Michigan. There are papers published by the Ogilvie group on this subject matter in the journal of physical chemistry as well. If interested, it is worth a look.

Source: http://chemwiki.ucdavis.edu/Physical_Chemistry/Spectroscopy/Fundamentals

/Selection_rules_and_transition_moment_integral

Electronic spectroscopy requires higher energies than previously studied vibrational and rotational spectroscopy.  Electronic spectroscopy caters to not only atoms or molecules but even ions, etc. When looking at the electronic energy levels, there is no analytical expression as it is different from vibrational and rotational spectroscopies. Instead, we can look at the energy levels in terms of potential energy surfaces. When looking at the potential energy diagrams, the Franck-Condon Principle goes into effect. The Franck-Condon Principle states that the transitions occurring between the electronic states corresponds to the vertical lines on the energy vs. internuclear distance diagram. The electronic transitions have a very short timescale compared to other methods. The Franck-Condon Principle provides a measure of the expected intensity for an electronic transition. The maximum for the absorption spectrum occurs at the transition energy corresponding to the largest Franck-Condon factors (transition intensity proportional to the square of the overlap integral). So the most intense electronic transitions occur where the upper electronic state matches and has the largest overlap with the lower electron states.

Understanding where the most intense electron transitions are supposed to occur was a little confusing until a clearer version of the Franck-Condon Principle diagram was seen. In the diagram (posted below), the electronic ground state and the electronic excited state are both listed. The vertical transition line can go from v0 to v10 or v12. The reason why it doesn’t go to the lowest state of the electronic excited state (v10) is because that transition doesn’t provide the most overlap possible. Also, on the diagram below, the line was not going straight. If it was to go straight, the most overlap is seen from the v12 level. The part that confused me in class was the curves that were drawn for each transition state. The maxima for each curve needed to match up in order for it to have the most overlap. Because the diagram below draws the curves in for each transition state, it is much easier to see why the vertical transition line follows such behavior. The information that is provided from the Franck-Condon Principle diagram is very relevant as it predicts where the most intense peak in a spectrum can occur at. It basically gives a reasoning to why the peaks are intense and where to look for them.

The website that I used came from a university which publishes many lectures/notes online. I believe that it is a valid source because it comes from an educational institution (UC Davis) and provides references/outside links. The two authors of the website are Zhou Lu and Chun-Yi Lin, both professors at the University of California, Davis. The information in the website does not seem biased as the main purpose was to educate students in the fundamentals of spectroscopy. The website covers a variety of relevant topics in chemistry including transition moments and selection rules.

condon

In order to accurately predict the geometric structure of molecules, the valence shell electron pair repulsion (VSEPR) model is used. Even though Lewis structures are useful in understanding the bonding of a molecule by representing the localized bonds and lone pairs, it is not able to predict the actual geometry of the molecule. The VSEPR model was created by Gillespie and Nyholm. Even though the VSEPR model isn’t quantitatively based, the model is still used today to accurately predict the geometry of molecules. Some assumptions were made for this model to work. When looking at the central atom of a molecule, the attached ligands and lone pairs naturally repel on another so they arrange in such a way to maximize their angular separation. Surprisingly, a lone pair occupies more angular space than a ligand. A multiply bonded ligand will occupy more space than a singly bonded ligand as well. For the most part, this model is accurate for examining the structure of a large number of molecules. However, one example where it won’t work as well is when we take a look at a radical such as CH3. CH3 has an unpaired electron which makes its electron geometry planar.

Although students in physical chemistry shouldn’t have a difficult time understanding the VSEPR model and how it is used, introducing the concept to beginners can be more of a challenge. Therefore, the plastic egg model is used and is implemented at Arizona State University. The commonly used balloon method was used previously where the balloons were connected by rubber bands and it demonstrated the octahedral geometry first. By popping a balloon one by one, the next lowest geometry was demonstrated. Also, it isn’t possible to show how the trigonal bipyramidal model can be derived from the linear model as the balloon method isn’t reversible. Plastic eggs are bought and separated in half. The correct way the eggs should look for the linear and trigonal planar geometry are shown in the picture below. Pairs of connected eggs represent atomic p orbitals. Appropriate color coding can represent the different lobes. SN1 and SN2 reactions can both be demonstrated by this plastic egg model. For example, the leaving groups and nucleophiles can be color coded and half an egg can be replaced by another. For VESPR, the ability to distinguish lone pairs from bonds and particular bonds from each other by colors makes this plastic egg model both affordable and reliable to teach the basic concepts of the VESPR model.

The article was found in the Journal of Chemical Education on the ACS website. The authors were Dr. Abbassian and Dr. Birk from the Arizona State University. The article was written in July 1996 so it is a bit outdated but gives a reasonable method to teaching the VESPR model as it hasn’t really changed since that time. The article seems biased in the sense that it is disregarding other teaching methods for the VESPR model but that was the whole point of the article. I believe that it is a reliable as it comes from the Journal of Chemical Education.

egg

Friedrich Hund deduced Hund’s rules which are used extensively today. The rules states that for a given configuration, the lowest energy term is that which has the greatest spin multiplicity and is determined by 2s+1. For example, the 3P term is of a 2p2 configuration is lower in energy than its 1S term. Another rule is that for the terms that have the same spin multiplicity, the term with the greatest orbital angular momentum (L), is the ground state and lies lowest in energy. For example, when comparing 1D vs 1P, the 1D term is the ground state term. The number of unpaired electrons should be maximized as well. Once the number of unpaired electrons is maximized, the term symbols for the specific atom or ion can be easily solved. Hund’s rules works best for the determination of the ground state of an atom or molecule.​

Hund’s rule is valid for many cases, but not all cases. There is a common misinterperation in the theoretical foundation of Hund’s rule. The traditional explanation of the rule is based on the Pauli exclusion principle where only the role of repulsion between electrons matters. The singlet state has higher energy than the triplet state. However, based on energetic analysis, that explanation is wrong. The average distance between electrons in the triplet state is actually smaller than the average distance between electrons in the singlet state. In actual netural atoms and small molecules, the energy difference is dominated by the energy differences in electron-nuclear attractions. Traditionally, it was the energy difference between interelectron repulsions. When a system is lowered from the singlet to the triplet state, an orbital contraction is seen. The contraction gives rise in the systematic kinetic energy and the electron repulsion and electron-nuclear attraction energy. The attraction energy will lower the systematic total energy and this is the physical basis of Hund’s rule.

This article was found in the Journal of Chemical Education and it was written by Ni Shenkaun from Anhui Normal University. Because it is a publication from the American Chemical Society, this paper is a valid source. The paper might be a little outdated as it was published in 1992. The paper discusses how the traditional theory behinds Hund’s rule actually was misinterpreted and included other parts including the electron-nuclear attraction energy. Therefore, this paper doesn’t seem too biased because it was trying to expand on  the theory behind Hund’s rule.

Source: http://pubs.acs.org/doi/pdf/10.1021/ed069p800

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