Diatomic Molecules: Degrees of Freedom and Equipartition of Energy

Chemistry, Physics
[caption id="attachment_24378" align="alignright" width="480"] A useful, but rough working model[/caption] Diatomic molecules have three translational degrees of freedom – but they have rotational and vibrational varieties as well. How do all these degrees of freedom relate to the distribution of molecular energy? To Begin With The location of any particle lies within three-dimensional space. The direction in which a particle moves is described by the three variables, usually written X, Y, and Z. As Ken Koehler of the University of Cincinnati informs us, atoms may be viewed as single points without size – so there are only three translational degrees of freedom for a given atom. Degree of Freedom of Diatomic Molecules Although it’s tempting to assume only three degrees of freedom exist for all “particles,” such is not the…
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Cooling Atoms to Millionths of 1 Degree by Laser?

Physics, Technology
[caption id="attachment_24362" align="alignright" width="480"] Laser trapped erbium atoms. Image by NIST[/caption] Laser cooling refers to a variety of techniques. The most common method is Doppler laser cooling. But cooling atoms by laser? Although the math and physics are challenging, we can understand the idea and basic mechanism more easily when we introduce three basic concepts first: quantum absorption of energy, the Doppler effect, and how atomic motion correlates with temperature. The Absorption of Energy "Quanta" It is at the very heart of the quantum theory that an electron bound in an atom cannot absorb just any amount of energy it encounters. In the free state, it can, but as soon as the electron is restrained as part of a new structure in an orbital, only certain discrete amounts of energy…
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Muonium: An Atom Similar to Hydrogen, Only No Protons!

Chemistry, Physics
[caption id="attachment_23970" align="alignright" width="480"] No proton![/caption] You heard correctly! From cosmic ray bombardments and particle accelerator experiments comes “muonium,” an other-worldly form of atom that, to a degree, resembles hydrogen. This atom is fascinating research scientists, along with another oddball, positronium. An Exotic Element… Sort Of There are some 90 naturally-occurring elements on Earth. There are more than a dozen other artificial elements, as well. Muonium is artificial, but not in the usual sense of the term. All of the more than one-hundred elements found in the periodic table consist of atoms made up of electrons traveling in orbitals about respective nuclei containing one or more protons and neutrons. Though muonium does have an electron orbiting a nucleus, it possesses no proton or neutron. Instead, it’s nucleus consists of an…
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Beer Bottle Condensation: What Forces Produce Droplets?

philosophy, Physics
Dan asked us¹... "My question concerns condensation droplets. What dictates how droplets form, then combine with each other? When you blow warm breath onto a cool surface, at first nothing appears to happen. Keep it up and droplets appear. These small droplets merge into bigger droplets. What physical laws dictate how this occurs? Also, what role does gravity play on vertical surfaces such as a chilled bottle of beer, producing tiny rivulets of moisture running down the sides?" Initial Commentary The answer, which follows, although it has some basis in well-known physical principles, depends in part upon observation, mental visualization, and (finally) blatant speculation. This is an interesting procedure, since so many of life’s mundane occurrences are in reality quite fascinating when closely examined. Initial Condensation We breathe in and…
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Which are Stronger? Covalent or Ionic Bonds?

Chemistry, Physics
Almost all the atoms found in nature, left alone to themselves, are stable structures. If they always remained such, there would be no need of chemists. Fortunately, when in close contact, atoms can react in a number of ways. Often they link to each other in various combinations through bonding, forming molecules called compounds. Such interaction requires explanation, and so provides employment to humans educated in this field: The field called chemistry. Chemical Bonds: Ionic and Covalent There are a variety of ways atoms bond to one another. Some bonds are weaker, and some are stronger. Two of the strongest forms of chemical bond are the ionic and the covalent bonds. Chemical bonds form between two atoms, each with its own electron environment. If each of the two atoms shares…
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Ions are Stabilized by Spreading the Electric Charge

Chemistry, Physics
[caption id="attachment_23719" align="alignright" width="440"] This image depicts the spreading charge of a nitrate ion. Image by elpot[/caption] Ions are charged atoms or molecules. They may have a plus charge, a minus charge or – rarely – both. Examples of each are the positive sodium ion (Na+1), the negative bisulfate ion (HSO4-1) and the glycine zwitterion (or dipolar ion) (H3N+1‐CH2‐C(O)2-1). Spreading the electric charge will stabilize both positively and negatively-charged ions – but how does this work? Charge and Nature Even as “nature abhors a vacuum,” it likewise abhors a concentrated electric charge – lightning well illustrates this point. Although ordinary table salt exists in water solution as charged ions, those ions are not isolated as the above shorthand symbols would indicate. The ions are stable in water because the charge…
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Is Gravity in Atoms Significant? No. Prove It!

Mathematics, Physics
[caption id="attachment_23683" align="alignright" width="480"] Is there gravity in the atom?[/caption] Theories of the microscopic never seem to include reference to gravity in the atom. Should they? What do you think? Numbers don’t lie: The reality is, gravity inside the atom is pretty insignificant. Let’s look at this in terms of scale, and then examine the equations for determining gravitational pull. Atoms and our Scale of Reference It is the human tendency to draw conclusions – with reference to the extremely large and the extremely small – on the basis of what we experience in our scale of reference. In fact, much good science has been realized using such assumptions. But only much good science – by no means all. In fact, many of the most incredible discoveries have not been…
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The Fascinating Kitchen Physics of Boiling Water

Chemistry, Physics
[caption id="attachment_23534" align="alignright" width="480"] Image by Jeshoots[/caption] Cutting-edge science is fascinating. Yet the science of everyday life is anything but boring. Consider the simple act of boiling water on the kitchen stove. There are many factors that come into play leading to the production of steam. Let's take a close look at water as an individual molecule and as a cluster of interacting molecules. Water at the Molecular Level Water consists of one oxygen atom plus two hydrogen atoms. An atom of oxygen is much larger than one of hydrogen. Most hydrogen atoms consist of a lone electron in orbit about a single proton nucleus. Oxygen atoms have a much larger nucleus orbited by 8 electrons. Oxygen has a strong affinity for electrons. So it is an electronegative element. On…
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Simplifying Mathematics: Introducing Vectors and Vector Addition

Mathematics, Physics
[caption id="attachment_23153" align="alignright" width="480"] Magnetic vector force field[/caption] We all know how to add, subtract, multiply and divide ordinary numbers, even if basic units are attached to them such as gallons, apples, feet, tons, and so forth. 4+3 = 7 5 lbs x 3.2 = 16 lbs These two examples illustrate pure numbers in the first instance, and simple quantities in the second instance. Introducing Vectors: What About Direction? What if we toss in direction? Imagine a huge square, 5 miles on a side. We have to travel along the perimeter to travel from Point A to Point B, and then on to our destination, Point C (see the image). We thus travel 10 miles to reach Point C. If we could travel "as the crow flies", we would only…
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The Chemical Bond – What Model Can We Choose to Represent It?

The Chemical Bond – What Model Can We Choose to Represent It?

Chemistry, Physics
Atoms and molecules are small indeed. Until recently, catching even a glimpse an atom was impossible. It still is impossible to see a chemical bond. Despite that, we know quite a few chemical reactions and can predict how many more will turn out. But we could know ever so much more about the scientific world of the very small if we had a very close bond model. We will discuss three bond models that have been used in the past, and to some extent still are used. The rigid model The spring model The force / charge model See the images associated with article. Each depicts one of the models discussed below. The Rigid Model One can depict a diatomic molecule by joining two balls with a thin dowel rod.…
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