Leakage of X-ray radiation Suppose a sample of strontium-90 is stored in a lead container with lead walls. It is know that X-ray radiation may be detected outside the lead container. After some discussion with my peers, it seems that we have differing theories on how the X-ray radiation is formed.


*

*Beta particles emitted by the decay of strontium-90 collide with the walls of the container, and in the process emit photons. These photons, when energetic enough, have high penetration power and can penetrate the walls of the container.

*Similarly, the beta emission by the decay of strontium-90 produces photons, but the photons instead tunnel through the walls.


The first theory seems to show a picture of the emitted x-rays actually passing through the empty space between lead particles in the wall of the container. Under this theory, the term "penetration" is not well defined enough.
Under the second theory, it seems that quantum tunnelling is not directly applicable because there is no potential barrier involved.
Which would be the correct explanation, or is there a better explanation?
 A: Yes, beta decay of Sr-90 produces a 546keV beta (note that Y-90, the daughter nucleus, is also a beta emitter, but at 2.284MeV). This energetic electron can then produce bremsstrahlung x-rays from interactions with electrons. For a given x-ray energy, lead will have some absorption coefficient - really this is no different than visible light interactions with matter, its just that you don't think of lead transmitting photons since you can't see through it.  X-rays travel just fine, with some absorption coefficient depending on their energy.
I'll note that the recommended shielding for Sr-90/Yr-90 is actually 1/2" or more of plexiglass. For example, Sr-90/Y-90 has the note "Do not use lead foil or sheets as primary barrier! Penetrating bremsstrahlung x-ray will be produced!" So you should slip a plexiglass liner in your lead bucket.
A: I don't know what "penetration power" is or why quantum tunneling needs to be invoked.
Sr-90 decays entirely via beta emission with up to $0.546\ \mathrm{MeV}$ given to the electron, and its daughter isotope similarly decays with up to $2.28\ \mathrm{MeV}$ given to the electron.
These energy ranges are right around the $1.71\ \mathrm{MeV}$ of P-32, whose beta emissions are known to induce significant bremsstrahlung in lead. Bremsstrahlung can easily produce photons of energies similar to the incident energy of the charged particle.
Any photon will have some attenuation length dependent on the frequency and the material it is passing through. Here is the NIST chart for lead to stop photons. As you can see, the value of $\mu/\rho$ is about $0.5\ \mathrm{cm^2/g}$ for photon energies of $2\ \mathrm{MeV}$. At a density of $11\ \mathrm{g/cm^3}$, this means the attenuation length is about $5.7\ \mathrm{cm}$. Even a $10\ \mathrm{cm}$ thick lead wall will only stop about 80% of such photons.
Please do follow Jon Custer's answer and properly line the storage container.
