What is the definition of the half-life of a radioactive element? -> The unstable atoms of the same species (same chemical element) and of differe...

What is the definition of the half-life of a radioactive element?

-> The unstable atoms of the same species (same chemical element) and of different masses, called radioisotopes, do not perform all changes (emissions) at the same time.
-> The radiation emissions are made in an unforeseen way, and it is not possible to guess the moment when a certain nucleus will emit radiation.
-> However, for a large number of atoms, the number of transformations per second is proportional to the number of atoms that are about to transform at that instant.
-> The probability of decay per atom per second must be constant, regardless of how long it has existed.
-> The decay constant λ is the probability of decay per atom per second and is a characteristic of each element.
-> The activity of the sample can be obtained by the expression: A = λN, where N is the number of atoms in the sample.
-> The activity of the sample at the initial instant (t = 0 s) is A(ti) = A0.
-> The half-life (T1/2) is the time required for the activity of the sample to decrease by a value that is half the initial activity.
-> The half-life can be calculated by the expression: T1/2 = ln(2)/λ.
-> The half-life is a characteristic of each radioactive element.
a) The time required for the activity of the sample to decrease by a value that is half the initial activity.
b) The time required for the activity of the sample to decrease by a value that is one-third the initial activity.
c) The time required for the activity of the sample to decrease by a value that is one-fourth the initial activity.