The generalization of a mathematical puzzle
about some very unlucky
The generalization of a mathematical puzzle
about some very unlucky
Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, such as nuclear transmutation, and nuclear properties.
It is the chemistry of radioactive elements such as the actinides, radium and radon together with the chemistry associated with equipment (such as nuclear reactors) which are designed to perform nuclear processes. This includes the corrosion of surfaces and the behavior under conditions of both normal and abnormal operation (such as during an accident). An important area is the behavior of objects and materials after being placed into a nuclear waste storage or disposal site.
It includes the study of the chemical effects resulting from the absorption of radiation within living animals, plants, and other materials. The radiation chemistry controls much of radiation biology as radiation has an effect on living things at the molecular scale, to explain it another way the radiation alters the biochemicals within an organism, the alteration of the biomolecules then changes the chemistry which occurs within the organism, this change in chemistry then can lead to a biological outcome. As a result, nuclear chemistry greatly assists the understanding of medical treatments (such as cancer radiotherapy) and has enabled these treatments to improve.
It includes the study of the production and use of radioactive sources for a range of processes. These include radiotherapy in medical applications; the use of radioactive tracers within industry, science and the environment; and the use of radiation to modify materials such as polymers.
It also includes the study and use of nuclear processes in non-radioactive areas of human activity. For instance, nuclear magnetic resonance (NMR) spectroscopy is commonly used in synthetic organic chemistry and physical chemistry and for structural analysis in macromolecular chemistry.
A polymer is a large molecule, or macromolecule, composed of many repeated subunits. Due to their broad range of properties，both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass relative to small molecule compounds produces unique physical properties, including toughness, viscoelasticity, and a tendency to form glasses and semicrystalline structures rather than crystals.
The term “polymer” derives from the Greek word πολύς (polus, meaning “many, much”) and μέρος (meros, meaning “part”), and refers to a molecule whose structure is composed of multiple repeating units, from which originates a characteristic of high relative molecular mass and attendant properties。The units composing polymers derive, actually or conceptually, from molecules of low relative molecular mass. The term was coined in 1833 by Jöns Jacob Berzelius, though with a definition distinct from the modern IUPAC definition。The modern concept of polymers as covalently bonded macromolecular structures was proposed in 1920 by Hermann Staudinger, who spent the next decade finding experimental evidence for this hypothesis.
Polymers are studied in the fields of biophysics and macromolecular science, and polymer science (which includes polymer chemistry and polymer physics). Historically, products arising from the linkage of repeating units by covalent chemical bonds have been the primary focus of polymer science; emerging important areas of the science now focus on non-covalent links. Polyisoprene of latex rubber is an example of a natural/biological polymer, and the polystyrene of styrofoam is an example of a synthetic polymer. In biological contexts, essentially all biological macromolecules—i.e., proteins (polyamides), nucleic acids (polynucleotides), and polysaccharides—are purely polymeric, or are composed in large part of polymeric components—e.g., isoprenylated/lipid-modified glycoproteins, where small lipidic molecules and oligosaccharide modifications occur on the polyamide backbone of the protein
In organometallic chemistry, a sandwich compound is a chemical compound featuring a metal bound by haptic covalent bonds to two arene ligands. The arenes have the formula CnHn, substituted derivatives (for example Cn(CH3)n) and heterocyclic derivatives (for example BCnHn+1). Because the metal is usually situated between the two rings, it is said to be “sandwiched”. A special class of sandwich complexes are the metallocenes.
The term sandwich compound was introduced in organometallic nomenclature in the mid-1950s in a report which confirmed the structure of ferrocene by X-ray crystallography. The correct structure had been proposed several years previously by Robert Burns Woodward and, separately, by Ernst Otto Fischer. The structure helped explain puzzles about ferrocene, the molecule features an iron atom sandwiched between two parallel cyclopentadienyl rings. This result further demonstrated the power of X-ray crystallography and accelerated the growth of organometallic chemistry.
The best known members are the metallocenes of the formula M(C5H5)2 where M = Cr, Fe, Co, Ni, Pb, Zr, Ru, Rh, Sm, Ti, V, Mo, W, Zn. These species are also called bis(cyclopentadienyl)metal complexes. Other arenes can serve as ligands as well.
Some mixed cyclopentadienyl complexes are M(C5H5)(CnHn). Some examples are Ti(C5H5)(C7H7) and (C60)Fe(C5H5Ph5) where the fullerene ligand is acting as a cyclopentadienyl analogue.
Sandwich complexes are even known containing purely inorganic ligands.
What is one physical characteristic of a solid? Solids can be hard like a rock, soft like fur, a big rock like an asteroid, or small rocks like grains of sand. The key is that solids hold their shape and they don’t flow like a liquid. A rock will always look like a rock unless something happens to it. The same goes for a diamond. Solids can hold their shape because their molecules are tightly packed together.
You might ask, “Is baby power a solid? It’s soft and powdery.” Baby power is also a solid. It’s just a ground down piece of talc. Even when you grind a solid into powder, you will see tiny pieces of that solid under a microscope. Liquids will flow and fill up any shape of container. Solids like to hold their shape.
Atoms are still energetic, jiggle, and the electrons move in solids, but the atoms are locked in position. In the same way that a large solid holds its shape, the atoms inside of a solid are not allowed to move around too much. Atoms and molecules in liquids and gases are bouncing and floating around, free to move where they want. The molecules in a solid are stuck in a specific structure or arrangement of atoms. The atoms still vibrate and the electrons fly around in their orbitals, but the entire atom will not change its position.
Acid/Base chemistry began with the Arrhenius model of acids and bases. This model states molecules in water that release hydrogen ions (H+) are acids, while molecules in water that release hydroxide (OH-) are bases. This is not complete. The current common definition of an acid and a base is based upon how the substance releases or attracts hydrogen ions (H+). Acids release H+ ions that can turn neutral molecules into positively charged ions, while bases can attract H+ ions from neutral molecules to produce negatively charged ions. This definition allows for bases such as ammonia which does not contain a hydroxide ion.
In water solutions, acids affect water molecules, producing hydronium (H3O+) and bases also affect water molecules, producing hydroxide (OH-) ions. The relative strength of acids and bases is measured by their respective ion concentrations once dissolved. The product of the hydronium ion (H3O+) concentration in water times the hydroxide ion concentration equals 1*10 to the -14th power. When water is not the solvent, the product of the concentrations of the positive and negative ions produced by acids and bases also has a constant value, but the value is different for each solvent.
In water solutions, the pH is equal to the negative log of the hydronium ion (H3O+) concentration. The pOH is equal to the negative log of the hydroxide ion (OH-) concentration. For typical solutions, pH varies between 0 and 14, with 7 (the pH of water) as neutral. Each “step” below 7 is ten times more acidic (since it was derived from a power of ten). For concentrated solutions (> 1 M) of strong acids or bases, solutions can have pH below 0 or above 14 respectively. However, considering the water system at 25 °C, the pH plus pOH of a substance is equal to 14.
The notion of pH in fact depends on the considered solvent and can be extended to other non aqueous polar solvent systems with different autoprotolysis constant. In this case, the sum of pH and pOH is equal to the value of -log of this constant.
For acids and bases that fit the Arrhenius model, a reaction between them always produce water and a salt. Reactions between acids and metal always produce a salt and hydrogen gas.
A buffer is a solution that can resist pH change upon the addition of an acidic or basic components. It is able to neutralize small amounts of added acid or base, thus maintaining the pH of the solution relatively stable. This is important for processes and/or reactions which require specific and stable pH ranges. Buffer solutions have a working pH range and capacity which dictate how much acid/base can be neutralized before pH changes, and the amount by which it will change.
To effectively maintain a pH range, a buffer must consist of a weak conjugate acid-base pair, meaning either a. a weak acid and its conjugate base, or b. a weak base and its conjugate acid. The use of one or the other will simply depend upon the desired pH when preparing the buffer.
A buffer is able to resist pH change because the two components (conjugate acid and conjugate base) are both present in appreciable amounts at equilibrium and are able to neutralize small amounts of other acids and bases (in the form of H3O+ and OH-) when the are added to the solution. To clarify this effect, we can consider the simple example of a Hydrofluoric Acid (HF) and Sodium Fluoride (NaF) buffer. Hydrofluoric acid is a weak acid due to the strong attraction between the relatively small F- ion and solvated protons (H3O+), which does not allow it to dissociate completely in water. Therefore, if we obtain HF in an aqueous solution, we establish the following equilibrium with only slight dissociation
A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.
The density of a liquid is usually close to that of a solid, and much higher than in a gas. Therefore, liquid and solid are both termed condensed matter. On the other hand, as liquids and gases share the ability to flow, they are both called fluids. Although liquid water is abundant on Earth, this state of matter is actually the least common in the known universe, because liquids require a relatively narrow temperature/pressure range to exist. Most known matter in the universe is in gaseous form (with traces of detectable solid matter) as interstellar clouds or in plasma form within stars.