Would my house's wall stop gamma rays? I'm wondering if there is a material which is able to stop all the electromagnetic spectrum's radiations. Something able to stop every electromagnetic radiation from the ones with the lowest frequency up to the one with the highest.
Intuitions tells me that it may depend on material density, as well as its thickness, but I couldn't find confirmation yet.
Are there any common material/element that are able to do it?
Are standard house walls able to stop them?
I would love some examples, like a paper of "this material", which is "this thick"...
 A: Whether or not a material stops or admits EM radiation is not an all-or-nothing affair. As you surmise, it depends on both material and on the frequency of radiation directed thereat, but what also holds is that all EM radiation will penetrate most everything to at least some depth which depends on both the frequency and the material type, which is characterized by a parameter known as the optical depth and, moreover, this depth is not all-or-nothing either: if $\mathrm{OD}(m, f)$ is the optical depth of a material of type $m$ and frequency $f$ of directed radiation against that material, then what that represents is the thickness of material which will cut the radiation intensity by a factor $\frac{1}{e}$, or about 63%. For example, if the optical depth is 1 mm, then the radiation directed against that material will be cut to 37% in the first 1 mm of material, then to 23% in the second 1 mm (2 mm of material "elapsed"), 15% in the third 1 mm (3 mm thick), and so forth, i.e. it's an exponential decay curve:
$$I(I_0, m, f, d) := I_0 \cdot e^{-d/\mathrm{OD}(m, f)}$$
where $I_0$ is the incident radiation intensity and $I$ is that at depth $d$ into the material. Every material has an optical depth greater than absolutely zero, even ones normally considered completely opaque like metals: in that case, it is related to what is called their "skin depth", and for visible light it is on the order of a wavelength.
Moreover, metals provide a good example to consider with regard to gamma rays specifically: generally speaking, a metal's skin depth (hence $\mathrm{OD}(m, f)$) is a decreasing function of the frequency $f$, i.e. higher frequencies penetrate less. But, above a certain point, which is called the metal's plasma frequency, the ability to absorb the radiation drops precipitously. Effectively, the reason the metals absorb radiation at lower frequencies is their copious highly mobile electrons are very responsive to the stimulation from the EM waves, but above a certain point, they are unable to move fast enough to keep up with the high-frequency oscillations and let it through. This frequency is around the petahertz (PHz) range, while gamma rays are in the exahertz (EHz) range or higher, i.e. greater than 1000 PHz, and typically more than $10^5$ PHz, and hence transmitted.
Your house's walls, if made of wood, are generally speaking very transparent to most gamma radiation, i.e. the optical depth is very large and considerably in excess of the typical wall thicknes. However, they are not absolutely so: while their optical depth may be "large", it is not infinite and hence some gamma rays will be absorbed. That is, they will "stop" them, just not stop very many, and probably not stop enough if, say, there was a nuclear blast outside close enough to be in the prompt gamma range, however in most cases that also means you are close enough the house and you will be vaporized in the heat and blast wave and hence you aren't going to worry about this (or anything else, for that matter). On the other hand, it COULD be a concern with a VERY small (not a mistake - as the devices get larger, blast and heat effects increase their lethal distance much faster than prompt radiation effects) device, like that a terrorist might use.
If a nuclear explosion is lit off far enough away from your house though as to avoid the immediate blast, heat, and prompt radiation, the kind of "radiation" you will be more concerned about will be that emitted by radioactive fallout: finely divided radioactive materials transported from the bomb site to your home on the wind. These have the problem that, as essentially dusts, they can seep in through various cracks in your house and you can then breathe them. And inhaled or ingested radioactive material is generally the worst since it spreads throughout your body and irradiates it internally.
I want to emphasize, however, that the above discussion pretty much only is about specifically EM radiation, and radioactive materials also emit particle radiation: massive particles that are typically electrons, positrons (though these are effectively instantly converted to gamma rays via annihilation with an electron) and "alpha particles" (fast-moving helium-4 nuclei). These radiations are considerably easier to stop than EM radiation, and in fact your house walls typically can resist them. But, as said, the chief danger would be fallout particles getting through the cracks and hence delivering the radiation directly to you, bypassing the walls altogether.
Insofar as to how to more effectively shield gamma radiation - the basic answer is to use some high-density and also high-atomic-number material, typically lead, but also bismuth (much less toxic than lead, but more expensive and a bit less dense), tungsten (very dense but not so good due to lower atomic number), and even uranium (that may seem a bit counterproductive, but natural [i.e. not processed into reactor/bomb fuel] and much less "depleted" uranium is actually a lot less radioactive than you might be thinking, and when you're resorting to this, whatever you've got inside is typically WAY "hotter".). The reason for this is that while the radiations are well above the metal plasma frequency and so are not going to be affected the same way, say, light, radio waves, etc. are, "higher-order" electromagnetic processes such as Compton scattering from individual electrons in the material, become important, and these materials, due to the fact of being dense, have lots of electrons in any given volume to provide lots of chances for a gamma ray to interact.
A: Not all of them no. The equation of interest is I = I0e(-pd) where d is the material thickness ,p is an attenuation coefficient of the material and I0 is the initial number of gammas hitting the wall. 'I' represents number getting thru. p will depend on the specific material and the energy of the gamma rays. Best materials are generally those with higher Z number (number of protons in nucleus - or the element) and the more dense the better. Lead is very good at stopping gammas but not good for construction. Brick would be better than wood. For gamma ray energies less than 10 MeV the brick would stop a large percentage of gammas. But that percentage would go down as energy goes up. You can probably find tables of attenuation coefficients on the internet. Or better yet graphs of attenuation coefficient vs gamma ray energy. If so its an easy calculation for 2 inches of wood and a half inch of dry board for example.
