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If I leave a bar of a radioactive material (e.g. uranium-235) for its half-life time, how will the bar look after halving its mass? Will it:

  • stay the same size, but be lighter?
  • shrink in size as to keep the same density?
  • be filled with small holes (like cheese or bread)?
  • have turned into a small pile of uranium dust as material holding the bar together has decayed?
  • or maybe something different?
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The title question cannot be answered generally, unless the naturl decay chain to the final stable particles is given , and the time.

Within the question the example of uranium 235 at its half life can be answered by looking at the natural decay chain :

u235chain

It is seen that it ends up in the stable lead 207, having lost through decays 38 nucleons. As alpha turns into a gas the material will be lighter by the ratio 38/235 . Radon is a noble gas, and it decays very fast into polonium, a metal. I do not think there will be time to create noticeable holes in the lattice by the radon leaving, as it decays very fast. Possibly the shape of the potential of the lattice may be affected. The stable end nucleus is lead which is a metal and will also occupy lattice locations. Maybe a specialist will answer with more details.

Other nuclei will behave differently, depending on their natural decay chain.

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  • $\begingroup$ I expect most of the $\alpha$ particles will be absorbed within the metal block, grab some electrons to form helium, and then the helium atoms stay stuck inside the metal for quite a while, until they diffuse to the surface and evaporate. $\endgroup$
    – Thomas Fritsch
    Commented Aug 1, 2020 at 12:43
  • $\begingroup$ The Wikipedia article says that He is trapped inside, but can migrate around. It collects in high pressure bubbles. The article talks about concentrations of decay products found in 50 year old U. So why isn't polonium one of those products? Does radon escape before decaying, even though He does not? $\endgroup$
    – mmesser314
    Commented Aug 1, 2020 at 14:59
  • $\begingroup$ @mmesser314 other articles on radon say they escape from uranium and thorium, and helium would escape easiar, as an alpha particle has kinetic energy from the decay. radon has a small probability of escaping because it decays in three days,nevertheless it is found in mines. $\endgroup$
    – anna v
    Commented Aug 1, 2020 at 15:48

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