The Half-Life of a Radionuclide

The half-life of a radionuclide refers to the time it takes for half of the atoms in a sample to decay. It is an important concept in nuclear physics and is used to describe the rate of radioactive decay. The correct answer to the given question is option 'B', which states that the half-life is the time in which N (the number of radioactive atoms) has been reduced to one-half of its initial value.

Explanation:

To understand why option 'B' is the correct answer, let's break down the other options:

a) The time in which N has been reduced to one-half of a standard fixed amount: This option is incorrect because the half-life does not depend on a standard fixed amount. Instead, it is a property of the radionuclide itself and remains constant regardless of the initial amount.

c) The time in which N has been increased to double its initial value: This option is also incorrect because the half-life is associated with radioactive decay, which involves the decrease in the number of radioactive atoms over time. It does not involve an increase in the number of atoms.

Now let's focus on option 'B', which is the correct answer:

b) The time in which N has been reduced to one-half of its initial value: This option accurately describes the concept of the half-life. When a radionuclide undergoes radioactive decay, the number of radioactive atoms decreases over time. The half-life is the time it takes for half of the atoms in a sample to decay, resulting in a reduction of N to one-half of its initial value.

For example, if a sample initially contains 100 radioactive atoms and has a half-life of 5 hours, after 5 hours, 50 atoms will remain. After another 5 hours, 25 atoms will remain, and so on. The time it takes for the number of atoms to halve is always the same, regardless of the initial amount.

Therefore, option 'B' accurately defines the half-life of a radionuclide as the time in which N has been reduced to one-half of its initial value.