Let’s say we have element X with half life of 100 years. Can chemical bonds like X−X or X−Cl increase/decrease half-life of X?
As a follow up question, can it increase/decrease radioactivity of X?
Let’s say we have element X with half life of 100 years. Can chemical bonds like X−X or X−Cl increase/decrease half-life of X?
As a follow up question, can it increase/decrease radioactivity of X?
It might depend on the type of decay undergone by the element, but certainly for some decays it is possible. That being said, these are the exception rather than the rule. Typically, nuclear decay is controlled by the weak nuclear force, which is mediated by the W and Z bosons in the Standard Model of Particle Physics. This is in contrast to chemical bonds arising from interactions between electrons, resulting from the electromagnetic force which is mediated by photons in the Standard Model. Any impact is primarily going to relate to the interactions between the pertinent quantum fields. Electrons can undergo processes guided by the weak nuclear force, so implicitly any impact to the electron's wavefunction will subtly—and occasionally noticeably—affect its ability to interact with the nucleus.
Different chemical bonds perturb the electronic environment of the nucleus, and thus any decay processes that are in some way dependent on the local electronic environment will have a shift in decay-rate, and thus a shift in half-life. The easiest example is electron capture. Electron capture is a decay process where an electron is captured by a proton and converted into a neutron. If the electronic wavefunction doesn't sufficiently overlap with where it needs to be for the weak force to mediate electron capture, then the decay rate will change. Here is a paper where the authors lengthen the half-life of a beryllium-7 atom by encapsulation with palladium atoms.
While I didn't see any examples in my (admittedly surface-level) search just now, I would also put forth that this likely holds for some other decay processes, such as beta decays. Beta decay occurs when a quark in a nucleon decays into a quark of the opposite type (called "flavor") and emits a W boson that itself decays either to a positron or to an electron* depending on if it was a proton $\rightarrow$ neutron decay (positron emission) or a neutron $\rightarrow$ proton decay (electron emission). Both of these processes produce a charged particle, and thus I imagine that screening of the local electron environment affects their rates (similar to how a chemical reaction is less favorable if there is a high activation energy, etc). Brief aside, all of this isn't particularly relevant for alpha decays (emission of a helium-4 nucleus) due to the fact this decay is due to interactions with the strong nuclear force and thus the impact of nuclear binding energy is significantly greater in magnitude than impact from the Coulombic interactions.
*and the relevant antineutrino
In reference to your final question, radioactivity is determined explicitly by decay process and decay rate—just like half-life—and so a shift in half-life would imply a shift in radioactivity a priori. The magnitude of change likely isn't enough that it would practically impair or accelerate radioactivity though, especially for the heavier elements where chemical bonding would be less relevant due to the larger role of valence electrons in chemical bonding than core electrons.
The half-life of a radioactive nucleus is not affected by the molecule or the ion containing this nucleus. It has been demonstrated plenty of times in the beginning of the 20th century.