## Describing Amounts of Work or Energy

We choose to measure things by volume, weight, or number based on what is convenient. We may work with a bulk measure such as a bushel of wheat or corn or apples. The volume of a filled bushel stays the same while the number of items changes. Or, we may think of a pound of butter or lead. The volume of a pound changes while the weight remains constant. Or, we may use numbers, and buy eggs by the dozen, paper clips in boxes of 100, and staples by the 1000.
Physicists, chemists, and biologists often choose to measure substances by the mole, a numbered unit of measure like the dozen, only bigger. A mole of many things is a reasonable amount. A mole of sugar, melted down, would about fill a soda can. A mole of water is about 1 tablespoonful. Most biochemists work with millimoles or micromoles of material because cells are too small to hold a mole of anything useful.
We don't commonly think of moles of energy packets, or about the amount of energy contained in a mole of something, but in fact that's what we need to do if we want to understand the processes that occur with photons. The energy contained in a mole of photons of a specified wavelength is measured with a unit of measure called the Einstein for solar radiation. The energy of a photon varies directly with its frequency and inversely with its wavelength. So an Einstein of light of the wavelength 250 nm contains exactly twice the energy of an Einstein of light of 500 nm. Each photon (each quantum) of 250 nm has twice the energy of a 500 nm photon. That means that the photon can do twice as much work. The equation used to find the energy in a mole of photons is E= hc/lambda where h is Planck's constant, c is the speed of light and is the wavelength of light. The value of E will come out in units that are useful for us to work with if we put the constants and wavelength in the proper units. Our choice of units depends on what we are trying to do. Biologists and physicists generally use different units.

Figure 1: Relationship Between Energies in two Different Units and Wavelengths.

The unit of measure for energy in biological systems is commonly the calorie. In nutrition we talk of the Calorie (large calorie or kilocalorie) which is 1000 calories. Your diet contains 1-3 thousand kilocalories per day.

A more systematic unit of measure is the Joule or kilojoule. One large Calorie is more than four kilojoules (kJ). An energy of 30 kJ equals about one mole of ATP; in other words, breaking the phosphate bonds in ATP under certain standard conditions releases 30kJ of energy that can be used to do work. You need at least five moles of ATP/hr to maintain your body functions (~900 Cal/ day). An Einstein of green light has an energy of about 200 kJ. Every day you use up the equivalent of more than 20 moles of green light. Because biological systems that capture light energy are imperfect, many more moles of photons must illuminate plant leaves before they can store the amount of energy you need every day. The energy not stored in producing sugars is released to the environment as heat.
The energy of rearranging or disassembling atoms and molecules is closely matched to the energies of radiation to which they are exposed. Molecules rotate or vibrate when exposed to far infrared photons with energies of a few kJ/mole, while near infrared with energy of up to 100 kJ/mole bounces the atoms around without breaking any bonds. Electrons are commonly excited into new orbits by visible light with energy up to 300 kJ/mole. Ultraviolet radiation, including the highest energy ultraviolet photons (vacuum ultraviolet)with energies up to 6000 kJ/mole, may knock electrons right out of the bond or even out of the molecule to which they are initially attached. X-rays and gamma rays have even more extreme effects on atoms and molecules.
For physical experiments we may use the electron volt (eV) rather than the joule (J) as a unit of measure, because on this scale of measurement we can conveniently talk about the energy of a single photon of light of a particular wavelength. One green light photon has an energy of a couple eV, while a mole of them has about 200 kJ of energy. Ultraviolet photons, depending on wavelength, have energy values in the range of several eV, up to 20 eV in the vacuum ultraviolet. The difference between the use of eV and J for comparing energies of photons is a constant, the Avogadro number. It's like talking of the difference in food value of an egg or a dozen eggs. We scale our units of measure according to our needs.
It is very difficult to directly measure, by chemical means, the effect of a single photon. Chemists and biologists, therefore, usually measure the effects of moles of photons and work with energy scales in kJ/mol. Physicists, on the other hand, do detect single particles, which may have energies of millions of eV each. It is possible to observe the effect of the impact of each individual photon of UV light. One UV photon may cause, with reasonable probability, an observable change of phenotype in a single cell of yeast. The sensitivity of yeast, therefore, makes them a valuable biological dosimeter.