Physics, mathematics. Final test paper 10. 1. Answer the question in detail: The law of radioactive decay. Half-life of radioactive element.

The law of radioactive decay, also known as the exponential decay law, describes the process by which unstable atomic nuclei lose energy by emitting radiation. This process is a random one, with the probability of decay increasing with the age of the nucleus. The law of radioactive decay can be mathematically expressed as:<br /><br />N = N0 * e^(-λt)<br /><br />where N is the number of undecayed nuclei at time t, N0 is the initial number of nuclei, λ is the decay constant, and e is the base of the natural logarithm.<br /><br />The half-life of a radioactive element is the time it takes for half of the nuclei in a sample to decay. It is a measure of the stability of the nucleus and is a constant value for each radioactive isotope. The half-life can be calculated using the formula:<br /><br />T1/2 = ln(2) / λ<br /><br />where T1/2 is the half-life and λ is the decay constant. The half-life is an important concept in nuclear physics and is used to determine the rate of decay of radioactive materials and to calculate the age of rocks and fossils.