What follows is a transcript of a letter my father sent to me when I was four years old, with annotations from me typing it up in italics but otherwise reproduced as faithfully as possible. It was written with a word processor and printed on dot matrix paper. My father was working in Indonesia while we were living in Australia. I only hope that if I ever have children, I can answer every question they have in this way.
24 February 1992, Monday, 7:08 am
Dear Bunky, [yes my nickname was Bunky]
It took the post office nearly one month to deliver Ima's letter [Ima is what I call my mother] with your question about how many atoms in an amoeba. The answer to your question is that there are about 12,000,000,000,000,000,000 atoms in an amoeba. This number can be called twelve pentillion (12 followed by 18 zeros).
I calculated the number of atoms based on a few things that we already know. These are:
The atomic weights of atoms: Hydrogen weighs 1 atomic weight unit (AWU), Carbon is 12 AWU, Nitrogen is 14 AWU, Oxygen is 16, Phosphorus is 31 and Sulfur weighs 32 atomic weight units. [Today I learned that this unit is called a dalton (Da); but IUPAC only approved that name in 1993.] These are the major atoms that make up the molecules in all living things. There are more than 100 different types of atoms which you can learn about in a chemistry book. There is one with a white cover on the shelves.
The gram-molecular weight (a Mole but not a furry one) of a substance contains about 6 x 1023 (6 with 23 zeros after it) molecules. This was calculated by a man named Avogadro. He is dead now but you can read about him in the encyclopedia. Gram molecular weight means that if you take the molecular weight of a compound (several atoms together) and weigh out that number in grams, you will have 600,000,000,000,000,000,000,000 atoms. [In fact it's that many molecules, but my father knew this; this is a slip of the tongue.]
For example: If carbon (charcoal) weighs 12 AWU, then 12 grams of charcoal should contain 6 x 1023 atoms. Water is a molecule with three atoms H2O or H-O-H. Ima has a computer program (I think called: Crystals) that will show you how molecules are made from atoms. Using the weights from paragraph one above you can see that one Mole of water weighs 18 grams and 18 grams of water contains 600,000,000,000,000,000,000,000 atoms. [In fact it's that many molecules, or 1.8 x 1024 atoms being that there are three atoms in each molecule. Maybe he didn't realize this distinction.]
The third thing that we already know that is useful to calculate the number of atoms in an amoeba is that one millilitre of water weighs about one gram. You will see how this is used in the calculation later.
So, here is how I calculated the number of atoms in an amoeba:
First we need to know the molecular weight of an amoeba. Amoebas are made up of many different kinds of molecules; it probably has one kind for its skin and others for the nucleus and the protoplasm. These molecules would be either carbohydrates, containing mostly Carbon, Hydrogen and Oxygen, or proteins containing those elements plus Nitrogen, Phosphorus, Sulfur and perhaps a few more. I estimate that the carbohydrate molecules will weigh about 250 AWU and the proteins about 500 AWU. [I'm not so sure that 500 AWU is a good estimate; most amino acids are around 150 AWU alone, and a protein will have hundreds of amino acids.] Like most living things, an amoeba will be mostly composed of water. So the average gram molecular weight of Amoeba can be calculated as follows, using the proportion of each substance to make up the average weight:
Substance Proportion Weight Contribution Water 90% 18 AWU 16.2 AWU Protein 5% 250 AWU 12.5 Carbohydrate 5% 500 AWU 25 TOTAL WEIGHT about 54 AWU
So that 54 grams of amoeba would have 6 x 1023 molecules. Now we need to calculate the number of atoms in an average amoeba molecule. [I knew he knew this difference.] We know that water has only 3 atoms in its molecule H-O-H. Proteins are fairly complex molecules and I would guess that the average amoeba protein molecule contains about 500 atoms of all the various elements. [Each with an average mass of 1 AWU? I say this is off by an order of magnitude, maybe two.] Carbohydrate molecules in amoebas are probably not so complex and contain about 250 atoms. Using the same table as above we can reckon that the number of atoms in an average amoeba molecule would be six.
Substance Proportion Atoms Contribution Water 90% 3 2.7 Protein 5% 36 1.8 Carbohydrate 5% 30 1.5 TOTAL Number of atoms per average molecule: 6
[This table doesn't really line up with the description in the paragraph above.]
So now we know that 54 grams of amoeba would have 6 x 6 x 1023 atoms in it. But how many amoeba are there in 54 grams? We can reckon that the average amoeba, if it would stop squirming around and putting out pseudopodia for a minute so it could be measured, might be 1 mm long, 0.3 mm wide and 0.2 mm high, or 0.00006cm3 in volume (cm3 is the same as ml on a measuring cup).
Now here is where the eight of water comes in handy. One ml (1 cm3) of water weighs one gram so that 0.00006 will weigh 0.00006 grams. We also know that the average molecule of amoeba, from paragraph 4 above, is 54 AWU which is exactly three times heavier than water, which weighs 18 AWU (see the second part of paragraph 2 above). 54/18 = 3. Therefore one amoeba should weigh 0.00018 grams (0.00006 x 3).
That means that there are 300,000 amoeba in 54 grams (54/0.00018 = 300,000). So now we have enough information to calculate the number of atoms inone amoeba since 300,000 amoeba will contain 6 x 6 x 1023 atoms (from paragraph 6 above). That means that one amoeba will have 12 x 1018 atoms or 12,000,000,000,000,000,000. Twelve quintillion atoms (divide the number of atoms in one Mole of amoeba by the number of amoeba in one Mole).
Abba [what I called my father]
Was this answer accurate? It's probably not far off, for giant amoeba; apparently 1014 is a good estimate for the number atoms in a human cell. I think his estimate of mass was an order of magnitude too low, but also his estimate of size was an order of magnitude too high for most amoeba, but also the number of atoms per molecule was probably too low. Right to within a few orders of magnitude.
But I was four years old. The point wasn't to have the right answer. It was to teach me to love learning; and to emphasize the scale difference between biology and chemistry; and to show that there's a process you can follow to answer questions; and that often that process means going to reference materials to build on the work of those who came before.