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.