How long does it take to replace all of the atoms in our bodies?

At first, this may sound like a bizarre question in that people don't think of their bodies "changing atoms" even through they eat food & drinks every day, and breath air continuously. That food, drink & air, in addition to supplying energy, supplies material to allow our bodies to grow, heal wounds, and such. In a very real sense, "we are what we eat". For example, about every 16 days nearly 100% of the water is exchanged in a healthy body.

As reported by Paul C. Aebersold on page 232 of the 1953 Annual Report of the Board of Regents of the Smithsonian Institution, radioisotope tracer experiments performed in the 1940's and early 50's showed that 98 percent of the atoms in a personís body change out every year.  Different molecules (& atoms) cycle through at different rates. As mentioned above, about every 16 days nearly 100% of the water is exchanged in a healthy body. In 1-2 weeks, half the sodium in our bodies is replaced. Half of the carbon in our bodies is replaced every 1-2 months. To quote from Aebersold's report,

"Indeed, it has been shown that in a year approximately 98 percent of the atoms in us now will be replaced by other atoms that we take in in our air, food, and drink."

What does this mean? In simplest terms, if 98% of the atoms in our bodies are replaced in a year, then after the first year, 2% are left. After the second year, 2% of 2%, or 0.04% are left. After the third year, 2% of  2% of 2%, or 0.0008% are left, etc. A table out to 20 years would look like this:

Year Fraction of Atoms Left Percent of Atoms Left
0 1 100 %
1 0.02 2 %
2 0.004 0.4 %
3 0.000008 0.0008 %
4 0.00000016 0.000016 %
5 3.2 x 10-9 3.2 x 10-7 %
6 6.4 x 10-11 6.4 x 10-9 %
7 1.28 x 10-12 1.28 x 10-10 %
8 2.56 x 10-14 2.56 x 10-12 %
9 5.12 x 10-16 5.12 x 10-14 %
10 1.024 x 10-17 1.024 x 10-15 %
11 2.048 x 10-19 2.048 x 10-17 %
12 4.096 x 10-21 4.096 x 10-19 %
13 8.192 x 10-23 8.192 x 10-21 %
14 1.6384 x 10-24 1.6384 x 10-22 %
15 3.2768 x 10-26 3.2768 x 10-24 %
16 6.5536 x 10-28 6.5536 x 10-26 %
17 1.31072 x 10-29 1.31072 x 10-27 %
18 2.62144 x 10-31 2.62144 x 10-29 %
19 5.24288 x 10-33 5.24288 x 10-31 %
20 1.04858 x 10-34 1.04858 x 10-32 %

The data in the above table, plotted on a semi-log plot, looks like this:

As a reminder to those of you who had High School Chemistry, the significance of having a fraction drop below the inverse of Avogadro's Number (6.022 x 1023), which is about 1.66 x 10-24, would signify when statistically there would be no original atoms left in a mole of atoms. A 70kg (about 154 lbs) human body has about 7 x 1027 atoms in it (about 10,000 moles). Statistically, there would be no original atoms when the fraction drops below 1/(7 x 1027), which is 1.43 x 10-28. According to our table above, we'd reach this point for our 154 lbs body a few months into the 16th year. Now some people weigh less and some people weight more than our 154 lbs example. If we cut the weight to say, 40kg (about 88 lbs), that would cut the number of atoms down to about 4 x 1027 atoms. Statistically, there would be no original atoms when the fraction drops below 1/(4 x 1027), which is 2.5 x 10-28. According to our table above, we'd also reach this point for our 88 lbs body a few months earlier into the 16th year. If we doubled the weight to 140kg (about 308 lbs), that would double the atoms to 1.4 x 1028 atoms. Statistically, there would be no original atoms when the fraction drops below 1/(1.4 x 1028), which is 7.14 x 10-29. According to our table above, we'd reach this point for our 308 lbs body is about half way between the 16th & 17th years.

So how long does it take to replace all of the atoms in our bodies? Answer: 16 to 17 years.

One can have even more fun with this issue, once one thinks of it in terms of Theseus's paradox, which considers whether something that has had all of it's components replaced one by one, is in the end, really the same object. There is a great video about this in terms of the transporter of Star Trek made by C.G.P. Grey, which you can view here:

 

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Additional Info:

   

1953 Annual Report of the Board of Regents of the Smithsonian Institution

How many atoms are in the human body?

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