The half`-`life of a radioactive isotope is always. `…………………………`.

Answer

**Step-by-Step Solution:**

1. **Understanding Half-Life**: The half-life of a radioactive isotope is defined as the time required for half of the radioactive substance to decay. This means that if you start with a certain amount of a radioactive isotope, after one half-life, only half of that amount will remain.

2. **Constancy of Half-Life**: One of the key characteristics of the half-life of a radioactive isotope is that it is always constant. This means that regardless of how much of the isotope you start with, the time it takes for half of it to decay remains the same.

3. **Independence from Initial Amount**: The half-life is independent of the initial amount of the radioactive isotope. This means that whether you have a large quantity or a small quantity of the isotope, the half-life does not change.

4. **Mathematical Representation**: The half-life (T_half) can be mathematically expressed using the formula:
\[ T_{half} = \frac{0.693}{\lambda} \]
where \( \lambda \) is the disintegration constant, which is a measure of the probability of decay of the radioactive isotope.

5. **Conclusion**: Therefore, the statement can be completed as: "The half-life of a radioactive isotope is always constant."

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