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?

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.

The Arrhenius equation describes the temperature dependence of reaction rates for many chemical reactions. It states that the rate of a reaction increases as the temperature increases. This is because higher temperatures generally provide more energy to reactant molecules, allowing them to overcome the activation energy barrier and react more quickly.

However, the situation is different for radioactive decay. The half-life of a radioactive element is the time taken for half of the radioactive nuclei to decay. This decay process occurs randomly at the atomic level and is governed by the activity of the radioactive substance, not by chemical reactions.

The rate of radioactive decay is independent of temperature because it is not influenced by the Arrhenius equation or any other reaction mechanism. The decay of radioactive isotopes is a spontaneous and natural process that is based on the inherent instability of the nuclei. It is governed by the laws of quantum mechanics and nuclear physics, which are distinct from the principles that dictate chemical reactions.

In other words, radioactive decay is a nuclear process that does not involve molecular collisions or activation energy barriers like chemical reactions. Therefore, the Arrhenius equation, which describes the temperature dependence of chemical reactions, does not apply to radioactive decay. The half-life of radioactive elements remains constant regardless of changes in temperature or pressure.