Naked Science Forum
Life Sciences => Physiology & Medicine => Topic started by: EvaH on 23/03/2021 13:43:27
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Colin asks:
If human DNA were modelled so that every atom was the size of a bowling ball and clumped together as a sphere, how big would it be?
What do you think?
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A bowling ball is about 21.6 to 21.8 centimeters in diameter. Atoms vary in size, but carbon atoms have a covalent radius from 69 to 76 picometers (depending on the type of bond). That would be an equivalent diameter from 138 to 152 picometers. A centimeter is 10 billion times larger than a picometer, so you are talking about a magnification factor between 142 million and 159 million. I'll take the average at about 150 million.
According to my research, human DNA is about 1.8 meters long. If carbon atoms were the size of bowling balls, that would make the DNA 1.8 m x 150 million = 270 million m long (270 km long). The width of a DNA molecule is about 2 nanometers so 2 nm x 150 million = 300 million nm (0.3 m wide).
Figuring out how big a sphere of this would be isn't exactly straightforward, but I can estimate it by calculating the approximate volume of the DNA and then finding the equivalent volume for a sphere. I can model the DNA molecule as a kind of twisted rectangle with previously calculated length and width of the DNA plus the thickness of an atom. So that would be 270 million meters x 0.3 meters x 0.0217 meters = 1,757,700 cubic meters. We can then put that volume into this calculator: https://www.omnicalculator.com/math/radius-of-sphere#:~:text=Given%20diameter%3A%20r%20%3D%20d%20%2F,%2F%20(A%2FV)%20.
The result is a sphere with a diameter of about 150 meters. This is probably an underestimate, though, as the phosphate groups would be more than one atom in thickness and phosphorus atoms are larger than carbon atoms.