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Density blocks gamma radiation basically, it's just the amount of mass per square meter of ordinary materials that makes the difference. Since lead is very dense and inexpensive it is often the material of choice, especially for small setups. On larger installations one can rely on thick concrete walls and such instead.
Alpha radiation is very easy to block as it is, no special materials required there.
But with beta radiation things change a bit - high-atomic-mass materials like lead don't really work that well here. They do block the beta radiation, but re-emit part of the energy as x-rays which are still ionizing and dangerous.
For work with pure beta emitters, the safety equipment usually is not shielding by lead, but by half an inch thick perspex or something similar to that. You'll find equipment like that in any radiological lab that works with pure beta emitters.
Yes, and you'd be right on Beta electrons causing secondary emissions. This is why when making shielding, one laminates a number of materials together so as to avoid the situation of X-ray emissions from the bremsstrahlung. Higher energy beta from Y90/Sr90 is particularly problematic in this situation.
Pb shielding, sandwiched between 2 thick Polyethylene plastic sheet material is able to take care of this effect nicely.
the high density polyethylene blocks the beta from getting to the Pb shield and additionally protects against high speed Neutrons as PE is a hydrocarbon, the Pb protects against the higher energy Gamma rays as it has a high Z (atomic number). Other materials with high Z factor are Ti,Cu, Cr, V, Fe
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