Rates of chemical reactions usually depend on temperature and pressure. However, half-life of all radioactive elements is independent of both T and p. How can these decay rates be independent of T if we beleive in the Arrhenius equation?

Answer 1

The Arrhenius equation uses k1, k1, T1, T2, and the activation energy. For radioactive decays, the activation energy for an excited nucleus is not predictable and is present in small amounts. Here is a wikipedia site to read; especially, scroll down to "explanation" and read that entire section (it isn't long), then pay particular attention to this paragraph which I have copied from that.
http://en.wikipedia.org/wiki/Radioactive_decay

Copied from Wikipedia. Such a collapse (a decay event) requires a specific activation energy. For a snow avalanche, this energy comes as a disturbance from outside the system, although such disturbances can be arbitrarily small. In the case of an excited atomic nucleus, the arbitrarily small disturbance comes from quantum vacuum fluctuations. A radioactive nucleus (or any excited system in quantum mechanics) is unstable, and can thus spontaneously stabilize to a less-excited system. The resulting transformation alters the structure of the nucleus and results in the emission of either a photon or a high-velocity particle which has mass (such as an electron, alpha particle, or other type).
Hope this helps.