Photons in my Hand

Quiz: how many UV photons per second does the DNA in your hand absorb in a sunny day?

Any person reasonably educated should be able to make estimates. If I ask you how many rolls of toilet paper are consumed in your city per month, I’m sure that you may give me a good guess within a couple of minutes.

Of course, I’d worry about your mental health if you told me the exact answer. But the order of magnitude—whether they are thousands or millions—you should find well.

Sometimes, however, we just don’t have enough information to even given an educated guess. How many worlds holding any kind of intelligent life are there in our galaxy? To guess one world is as good as to guess one million. (To guess zero world might be a bit too cynical though.)

There are times the information is available, but it’s so specialized and out of usual contexts that we just can’t guess. For example: When you are out in a sunny day, how many photons per second are absorbed by all DNA in your right hand?

I’ve been asking that question myself. It’s a kind of professional curiosity. Although I’ve been working with simulations of UV absorption by organic molecules for years, I confess I didn’t have any clue on the answer. What would you say, are they 10, 1000, or 1 million UV photons per second absorbed by the DNA in your hand?

And if you are wondering why such information would bear any relevance, just think that the energy of these photons may damage DNA, causing cell death, mutations, and cancer. Relevant enough?

Well, I did my homework and by the end of this post you will know this number as well.

To do this estimate, I needed two basic non-trivial pieces of information: a) the solar irradiance, which is how much solar power at a certain wavelength reaches each unity of area of Earth’s surface; and b) the DNA absorptivity, or how much radiation a certain amount of DNA absorbs.

It’s not difficult to find out either of them. Wikipedia has a good entry on solar irradiance. DNA absorptivity needs some deeper digging, but it isn’t too difficult to find either.

Having those quantities and some basic notions on cell sizes, to estimate that number of photons isn’t hard.

Starting nerd section – you may skip it…

On the one hand, DNA is a good UV chromophore, with maximum absorption at 260 nm. Sun light, however, is weak in this wavelength thanks to the ozone layer, which screens UV radiation before it reaches the surface. On the other hand, the peak of solar radiation is at the visible range, but there DNA doesn’t absorbs much.

The optimal absorption/radiation point is at about λ = 290 nm. For this wavelength, solar irradiance is I = 10-9 Watt per m2 per nm and the DNA molar absorptivity is ε = 1000 liters per mol per cm.

The number P0 of photons within a range δλ around λ, reaching an area A per unit of time, is
P0 = IAδλ/Ep,
where Ep = hc/λ is the energy of a single photon. (Later I will take δλ = 2 nm.)

After crossing a path L of a certain substance, the Beer-Lambert law tells that the number of photons emerging at the other side is reduced to
Pd = P0 10εcDNAL,
where  cDNA = N/VNA is the molar concentration of DNA, or how many moles of DNA are within a volume V.

To finish my estimate, I just need some basic geometric approximations on where DNA is stored.

DNA coils itself into chromosomes filling the cell nucleus. Within each single nucleus, there are N = 6.4×109 nucleobases (twice the number of base pairs in our genome); each nucleobase itself is able to absorb UV.

The nucleus has diameter d = 10 μm and we can use this information to suppose that the UV radiation reaches a circular area A = πd2, that DNA fills a spherical volume V = πd3/6, and that radiation crosses a path L = d within the nucleus.

Thus, the number of UV photons absorbed by DNA per second per cell is
ΔP = P0Pd = πd2Iλδλ/hc × (1-10-6εN/πNAd2).

Ending nerd section – sorry for that…

Replacing all the figures I gave above for the variables in the last equation (after converting all the units to the same system, of course) gives 0.04 UV photons absorbed per cell per second.

Not very impressive, you might say. Nevertheless, if we take into account that the area of a skin cell is 10-9 m2 and the area of a hand is 0.01 m2, there are 10 million cells directly exposed to the sun. Therefore, the DNA in a single hand dangling around in a sunny day is absorbing something like 400 thousand UV photons per second!

This is a crude estimate, naturally. I didn’t consider the screening of UV by melamine, urocanic acid, histones, and other substances also absorbing UV and in this way protecting DNA. I also didn’t consider absorption at deeper cell layers or out of the 290-nm range.

But, anyway, hundreds of thousands of photons absorbed per second. Each of them potentially carrying a hurtful seed of a skin cancer. I don’t want to sound like a paranoid hypochondriac, but this number gives a good reason to not forget the sunscreen.


  • Do you want to known how DNA coils within the nucleus? This video gives a nice introduction on that.

Categories: Chemistry, Science

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