I received a request from eliza_k on IHIQS to discuss the dangers of ionizing radiation at a site of nuclear fallout, "If gamma rays from space are absorbed by Earth's atmosphere without causing major harm, how do gamma rays (not in a vacuum) from something like an explosion exist long enough to do damage?" I realized on hindsight that my response did not answer the question at times, so I've edited this a little!
"I don't know the ideal answer to your question, but I hope you find my explanation acceptable: there are various factors which explain the difference.
Firstly, you have to understand how radiological damage is caused.
Let us first make the distinction between radiological and non-radiological damage that can be caused by radiation.
Suppose we're considering that the incident energy is only moderate. By this, I mean it is low enough such that it doesn't simply transfer energy to the extent that you 'burn up'; in which case, you can be harmed by even the least energetic of the electromagnetic spectrum: for instance, sticking your hand in front of a satellite dish, you'd find it charred, while keeping your hand beside a transmitting mobile phone forever would cause no such damage. Now, both forms of radiation are in the microwave region of the electromagnetic spectrum - and they are too low to cause excitations of bound electrons to upper states on individual atoms - and consequently, ionisation of human tissue. But one is able to cause damage: this is non-radiological damage. Other examples include experimental non-lethal weapons which employ radio waves to incapacitate a target.
Now, regarding the excitation explanation above, this process of ionization usually sets in at much higher frequencies: ultraviolet radiation, X-rays and gamma rays. This can be explained by looking at these mentioned lower bound states and upper bound states as quantized energy levels: a specific amount of energy is required to raise an electron from one state to another, and more accurately, to the 'infinite' state (not a huge number as you're led to believe by the term; the gap between this state and the 3th energy level could be as small as 2.4 * 10^-19 J, and consequently, the gap decreases, meaning you're closing in on our 'nth value denoting infinity' if you like, and the 4th energy level can have as little -1.4 * 10^-19 J.) By infinite, we mean the electron is outside of the electrostatic attraction of the nucleus, hence its potential energy is at its greatest: 0, taking negative values to be 'bound' by the nucleus. It doesn't matter what rate at which you bombard an atom with photons of a particular energy. Neither does the momentum matter: you could have comparable momentum imparted by visible light photons and electrons, but the electrons have greater energy and hence more likelihood that they are sufficient to ionize atoms in your tissue.
So it's entirely an issue of sufficient energy.
Distance
I say this first as you've already mentioned it. The intensity of radiation from the Sun incident upon the Earth is approximately inversely proportional to the square of the distance from the Earth. That means the rate of energy transfer onto your body from gamma rays emitted by the Sun is much lower - by a factor of (2.5*10^4)^2/(1.46*10^11)^2 ~ 10^-14. That's less than a trillionth. This, divided by the minimum (I'd prefer to say 'critical', but these two happen to be the same) photon energy for ionization is equal to your number of sufficiently energetic photons incident in a second. It's a much smaller number. And the nice part is that we are multicellular organisms: tissue consists of a huge number of atoms. Having a very small part of undergo ionization doesn't matter that much, so a small number of photons per second is acceptable. On the other hand, having smaller numbers wouldn't help if we were unicellular organisms - I hope you can see why now.
Shielding
About these cosmic gamma rays that reach the Earth - you forget that they have to pass through a very thick layer of atmosphere, where they are very likely to bombard on gases and lose their energies. It's the same idea as why gamma radiation cannot penetrate very thick concrete - they get attenuated. Above which, the atomic separation of lead kernels in the plate is very small, causing the scattering of the gamma rays away from its original trajectory.
On the other hand, although the mean separation between air molecules is relatively very large, with certain thickness, it is almost certain that no gamma rays reach the other end. The amount of atmospheric shielding between the Sun and you (~100km) is most definitely larger than the amount of shielding between the radioactive sources of a nuclear fallout and you, as I implicitly assume that you are referring to a person near the site of a nuclear fallout.
"Secondary" radiation
Actually, gamma rays don't have that much ionizing power. Compare photon energy E = hf and energy possessed by alpha particles, beta particles etc. and you'll find the latter much more energetic (mainly because they have mass - this can be quantiatively shown). They only tend to harm more because they travel further. But at point blank, you'd rather be exposed to gamma radiation than alpha particles at the same rate of incidence.
Similarly, what makes a site of nuclear fallout more harmfully 'radioactive' is due to the radioactivity promoted by the initial nuclear reactions. The products of these tend to be unstable, and they will eventually undergo decay (at random but with a certain half-life) to form a more stable product, while producing either alpha, beta or gamma radiation as by-products. They have a certain half-life, meaning that they will stay around ("exist long enough"). And these subsequent decays cause a lot of harm - not that the radiation from the explosion lingers around waiting to be absorbed.
On the other hand, due to the shielding and distance reasons above, these more harmful forms of radiation from cosmic sources, including the Sun, do not reach us."
"I don't know the ideal answer to your question, but I hope you find my explanation acceptable: there are various factors which explain the difference.
Firstly, you have to understand how radiological damage is caused.
Let us first make the distinction between radiological and non-radiological damage that can be caused by radiation.
Suppose we're considering that the incident energy is only moderate. By this, I mean it is low enough such that it doesn't simply transfer energy to the extent that you 'burn up'; in which case, you can be harmed by even the least energetic of the electromagnetic spectrum: for instance, sticking your hand in front of a satellite dish, you'd find it charred, while keeping your hand beside a transmitting mobile phone forever would cause no such damage. Now, both forms of radiation are in the microwave region of the electromagnetic spectrum - and they are too low to cause excitations of bound electrons to upper states on individual atoms - and consequently, ionisation of human tissue. But one is able to cause damage: this is non-radiological damage. Other examples include experimental non-lethal weapons which employ radio waves to incapacitate a target.
Now, regarding the excitation explanation above, this process of ionization usually sets in at much higher frequencies: ultraviolet radiation, X-rays and gamma rays. This can be explained by looking at these mentioned lower bound states and upper bound states as quantized energy levels: a specific amount of energy is required to raise an electron from one state to another, and more accurately, to the 'infinite' state (not a huge number as you're led to believe by the term; the gap between this state and the 3th energy level could be as small as 2.4 * 10^-19 J, and consequently, the gap decreases, meaning you're closing in on our 'nth value denoting infinity' if you like, and the 4th energy level can have as little -1.4 * 10^-19 J.) By infinite, we mean the electron is outside of the electrostatic attraction of the nucleus, hence its potential energy is at its greatest: 0, taking negative values to be 'bound' by the nucleus. It doesn't matter what rate at which you bombard an atom with photons of a particular energy. Neither does the momentum matter: you could have comparable momentum imparted by visible light photons and electrons, but the electrons have greater energy and hence more likelihood that they are sufficient to ionize atoms in your tissue.
So it's entirely an issue of sufficient energy.
Distance
I say this first as you've already mentioned it. The intensity of radiation from the Sun incident upon the Earth is approximately inversely proportional to the square of the distance from the Earth. That means the rate of energy transfer onto your body from gamma rays emitted by the Sun is much lower - by a factor of (2.5*10^4)^2/(1.46*10^11)^2 ~ 10^-14. That's less than a trillionth. This, divided by the minimum (I'd prefer to say 'critical', but these two happen to be the same) photon energy for ionization is equal to your number of sufficiently energetic photons incident in a second. It's a much smaller number. And the nice part is that we are multicellular organisms: tissue consists of a huge number of atoms. Having a very small part of undergo ionization doesn't matter that much, so a small number of photons per second is acceptable. On the other hand, having smaller numbers wouldn't help if we were unicellular organisms - I hope you can see why now.
Shielding
About these cosmic gamma rays that reach the Earth - you forget that they have to pass through a very thick layer of atmosphere, where they are very likely to bombard on gases and lose their energies. It's the same idea as why gamma radiation cannot penetrate very thick concrete - they get attenuated. Above which, the atomic separation of lead kernels in the plate is very small, causing the scattering of the gamma rays away from its original trajectory.
On the other hand, although the mean separation between air molecules is relatively very large, with certain thickness, it is almost certain that no gamma rays reach the other end. The amount of atmospheric shielding between the Sun and you (~100km) is most definitely larger than the amount of shielding between the radioactive sources of a nuclear fallout and you, as I implicitly assume that you are referring to a person near the site of a nuclear fallout.
"Secondary" radiation
Actually, gamma rays don't have that much ionizing power. Compare photon energy E = hf and energy possessed by alpha particles, beta particles etc. and you'll find the latter much more energetic (mainly because they have mass - this can be quantiatively shown). They only tend to harm more because they travel further. But at point blank, you'd rather be exposed to gamma radiation than alpha particles at the same rate of incidence.
Similarly, what makes a site of nuclear fallout more harmfully 'radioactive' is due to the radioactivity promoted by the initial nuclear reactions. The products of these tend to be unstable, and they will eventually undergo decay (at random but with a certain half-life) to form a more stable product, while producing either alpha, beta or gamma radiation as by-products. They have a certain half-life, meaning that they will stay around ("exist long enough"). And these subsequent decays cause a lot of harm - not that the radiation from the explosion lingers around waiting to be absorbed.
On the other hand, due to the shielding and distance reasons above, these more harmful forms of radiation from cosmic sources, including the Sun, do not reach us."
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