Q1: Calculate the frequency of each of the following wavelengths of electromagnetic radiation:

1. 632.8 nm
2. 503 nm
3. 0.052 nm

Q2: Calculate the wavelength of each of the following frequencies of electromagnetic radiation:

1. 104.3 MHz
2. 1035 kHz
3. 835.6 MHz

A: When solving these types of problems, it is important to remember that wavelength and frequency are inversely proportional. This means that as one value goes up, the other value goes down. We can solve frequency/wavelength problems using the formula , where v is the frequency, c is the speed of light, and lambda λ is the wavelength.

Since wavelength is often expressed in nm, it is helpful to know the speed of light in nm since this will minimize how many conversions we need to do when solving these problems. We know that the speed of light is . To find the speed of light in nm, we perform the following calculation:

Now we can use this speed of light when doing all our frequency/wavelength problems. We use the formula above, , and plug in the values we know. Then we can solve for the unknown variable.

632.8 nm

The nm units cancel out and we are left with seconds. The standard unit for frequency is cycles per second, denoted as Hz or . So we are left with .

503 nm

You try solving the last one for 0.052 nm before looking at the solution below.

0.052 nm

Solving for frequency requires a bit more thinking, but the basic concept is the same.

104.3 MHz

We need to convert MHz to Hz. The conversion unit we need is .

Now we can plug in our values and solve.

Now we cancel our units and solve to get

That’s not so painful, is it? Let’s try the next one.

1035 kHz

We need to convert kHz to Hz. The conversion unit we need is .

Now we can plug in our values and solve.

You try solving the last one for 835.6 MHz before looking at the solution below.

835.6 MHz

Now we can plug in our values and solve.

Now we cancel our units and solve to get

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A: When categorizing electromagnetic radiation, it is important to remember the following trends:

• Lower energy means a longer wavelength and lower frequency.
• Higher energy means a shorter wavelength and higher frequency.
• Visible light is approximately in the middle of the electromagnetic spectrum.

Write the types of electromagnetic radiation in order of shortest wavelength to longest wavelength:

• Gamma ray
• X-ray
• Ultraviolet
• Visible light (violet, indigo, blue, green, yellow, orange, red)
• Infrared
• Microwave
• Radio (cell, FM, TV, AM)

The order is the same to write the types of electromagnetic radiation in either increasing energy per photon or increasing frequency:

• Radio (AM, TV, FM, cell)
• Microwave
• Infrared
• Visible light (red, orange, yellow, green, blue, indigo, violet)
• Ultraviolet
• X-ray
• Gamma ray

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Amino acids are always composed of an amino group, a carboxyl group, and an R-group. Only the R-group ever varies. 20 different amino acids can be found in living organisms. Amino acids are connected to each other during the process of translation. Covalent bonds between several amino acids are called peptide bonds.

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Macromolecules are many smaller molecules bonded together to make polymer. Carbohydrates, proteins, and nucleic acids are a few examples of macromolecules found in living organisms. They tend to be large and complex (as far as molecules go). The smaller molecules used to build a macromolecule, or polymer, are called monomers.

The monomers used to build proteins are amino acids. They are connected by peptide bonds. Proteins have many functions, some of which include structure, organization, enzymes (catalyst reactions),  and transport.

The monomers used to build carbohydrates are called monosaccharides. They are connected by glycosidic bonds. Carbohydrates store energy, carbon, and give structure to plants and animals.

The monomers used to build nucleic acids are called nucleotides. They are connected by phosphodiester bonds. Nucleic acids include DNA and RNA.

The monomers used to build fats and lipids are called glycerol and fatty acids. They are connected by ester bonds. Fats and lipids function to store energy and provide structure for plants and animals. Triglycerides and phospholipids are important fats to know about for biology.

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Functional groups have chemical properties that are important to the structure and function of the molecules in which they are found. Each functional group holds onto its properties regardless of the molecule in which it is found.

The following are some important functional groups and where they are most likely to be found. All functional groups are formed by the base molecule listed below and an R-group.

• Amino – amino acids (proteins) | NH2
• Carboxyl – amino acids, fatty acids | COOH
• Hydroxyl – steroids, alcohol, carbohydrates, some amino acids  | OH
• Methyl – may be attached to DNA, proteins, and carbohydrates | CH3
• Phosphate – nucleic acids, ATP, attached to amino acids | PO4
• Sulfhydryl – proteins that contain the amino acid cysteine | SH

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Carbon is able to form four bonds with other atoms, enabling a variety of different combinations and possibilities for molecules and macromolecules, in a variety of structures and functions. All organic compounds contain carbon atoms bound to other atoms. Typically, carbon forms covalent bonds with other carbons, hydrogen, oxygen, nitrogen, and sulfur.

• Carbon and hydrogen have similar electronegativities and thus carbon-carbon bonds and carbon-hydrogen bonds are nonpolar.
• Molecules with mostly carbon-hydrogen bonds are called hydrocarbons and are not soluble in water.

To remember the electronegativity ratios for common organic compounds, don’t try to memorize the actual electronegativity. Instead, use the anagram ONCH. (Oxygen, Nitrogen, Carbon, Hydrogen) which can be expanded a bit:

O>>N>C=H

Oxygen is much much more electronegative than Nitrogen.

Nitrogen is more electronegative than Carbon.

Carbon is equally electronegative to Hydrogen.

More than one atom of the same type bonded together has a neutral electronegativity.

This will make it much easier to determine the relative polarity of organic molecules.

One last thing about carbon is its ability to form very stable bonds with other atoms that last through temperature changes. Because the carbon atom is quite small, the length of the bond with other atoms is short, which is more stable than a longer bond.

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If any of those circumstances describe you, then you will be interested in this bit of chemistry in action. L’oreal has developed ammonia-free hair dye that works equally as well as the formulations that contain ammonia. Previously, ammonia-free dyes could only change the color of hair by one shade. Not anymore! Check out the article from Scientific American for more details.

Observations: Hair dye will soon debut in U.S. that has the power of ammonia without the smell .

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Carbohydrates

Carbohydrates are water-containing carbon compounds. Starch and cellulose are examples of carbohydrates. Both starch and cellulose are built up from glucose. Thus, glucose is a monomer and starch and cellulose are polymers.

The simplest sugars are called monosaccharides (meaning “single sugars”.) The most common types are pentose and hexose sugars (having five and six carbons, respectively.) Common monosaccharides are glucose, galactose, and fructose.

When two monosaccharides become friends and link up, the result is a disaccharide (meaning “two sugars”.) When the monosaccharides bond, a water molecule is released. This is called a dehydration reaction in condensation chemistry, and the bond is called a glycosidic bond. When water is added back to the molecule, the link is broken and the disaccharide is broken into two monosaccharides again. Common disaccharides are sucrose, lactose, and maltose.

Lots of monosaccharides linking up with each other via condensation chemistry form polysaccharides (meaning “many sugars”.) Plant and animal cells contain the polysaccharides starch and glycogen, respectively. Starch and glycogen provide a store of energy for plants and animals. Glycogen is an especially efficient store of energy because it is highly branched and spider-webby. This makes it easier to fit a lot of it in small spaces. Starches are less branched and thus take up more space, and thus provide less energy efficiency. Many other polysaccharides play structural roles, such as cellulose in plants, chitin in insects, glycosaminoglycans in animal cartilage. Cellulose  is long and straight without any branching, so it can lay down flat like bricks on a house and contributes to the strength and insolubility of a plant.

Lipids

Lipids are fats, phospholipids, and steroids. They are nonpolar and thus are insoluble in water.

Fats are made up of triglycerides, which are glycerol molecules attached to three fatty acid molecules. Three water molecules are released (dehydration reaction) when the glycerol and fatty acids link up, and the bond is called an ester bond. The carbons in fatty acids can be said to be either saturated or unsaturated. This refers to how many single or double bonds are formed with the carbons. If all the carbons have only single bonds, the fatty acid is said to be saturated. If even one carbon has a double bond, the fatty acid is said to be unsaturated. We call carbon chains with only one double bond monounsaturated; if there is more than one double bond in the carbon chain, it is said to be polyunsaturated. Unsaturated fats have a “kink” in the chain due to the double carbon bond, causing the fat to stay in a liquid form, like olive oil. Saturated fats, like hamburger grease, harden at room temperature because there is no “kink” in the carbon chain to prevent the macromolecules from settling.

Phospholipids are very similar to tryglycerides, except that the glycerol molecule is attached to a phosphate group instead of a fatty acid, and the phosphate group is usually also attached to a charged nitrogen-containing molecule. This creates a polar, or hydrophilic, head and a nonpolar, or hydrophobic, tail. Phospholipids make up the plasma membrane of cells because of their amphipathic properties and are critical to supporting many of the functions in cells.

Steroids are very different in structure from triglycerides and phospholipids. All steroids are built on a four carbon rings. Usually, they are not attached to enough polar molecules to make them soluble in water. The most well-known steroid is cholesterol. Testosterone and estrogen are also steroids, lending credence to the “structure preceeds function” concept. Even the tiniest change in structure can lead to a very different function.

One more type of lipid is wax. Waxes are often found on plants, where they provide a protective barrier to prevent loss of water from the plant. This works because wax is extremely hydrophobic and thus keeps water inside the plant. Wax is also used to form the honeycomb of beehives, thus providing structural integrity.

Proteins

Proteins are built from amino acids- they are polymers of amino acids. They serve many different functions, such as protecting against disease, enzymatic reactions, assisting in movement of solutes into and out of cells, and many other things. Amino acids are made from a carbon linked to an amino group, a carboxyl group, a hydrogen atom, and a side chain called an R-group.

There are 20 different amino acids found in living organisms. Some are polar and charged, some are polar and uncharged, and some are nonpolar. Some are acidic, some are basic, and some are neutral. Thus, amino acids can serve many different functions depending upon their structure and properties.

The linking of amino acids to form proteins is another form of condensation chemistry. Every time two amino acids bond, a water molecule is released. The bond formed between a carboxyl and amino group (which forms an amino acid) is called a peptide bond. Thus, a chain of amino acids is called a polypeptide, referring to the peptide bonds. A protein is a functional unit comprised of one or more polypeptides that serves some particular function.

Proteins have four levels of structure. The primary structure is simply the chain of amino acids. There are 20 different amino acids, so the amino acids present in the protein and the order in which they are arranged constitutes the primary structure. The secondary structure is caused by hydrogen bonds formed between polar groups and the polypeptide backbone of the amino acid. Repeating patterns of amino acids will cause the polypeptide to fold up into either alpha helixes or beta sheets, which constitute the secondary structure. Tertiary structure is the complex, three-dimensional shape of a protein based on the bonding relationship between the R-groups of the amino acid. Bonding relationships can be affected by hydrogen bonds, polar interactions, ionic bonds, hydrophobic effects, Van der Waals forces, or disulfide bridges. An alpha helix or beta sheet further folds up on itself in a particular way to produce a characteristic pattern for a particular protein, which constitutes the tertiary structure. The final level of structure for proteins is the quaternary structure. Not all proteins have a quaternary structure. A quaternary structure can only occur when two or more proteins combine into a single structure to form an even more complex structure. Many proteins do not reach the quaternary structure and instead only reach tertiary structure. The way the different levels of protein structure interact to create consistent shapes for proteins is critically important to the function of the proteins. Even small changes in the protein structure can render the protein useless, or even harmful.

Nucleic Acids

Nucleic acids are split into two groups: deoxyribonucleic acid (DNA) and ribonucleic acid (RNA). They are the genetic information responsible for heredity and genetic variation in living things. The monomer of a nucleic acid is a nucleotide, which is composed of a phosphate group, a pentose sugar, and a base (adenine, cytosine, guanine, thymine, or uracil). DNA consists of two strands of nucleotides wound around each other to form a double helix. RNA consists of only a single strand of nucleotides.

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