Many unstable nuclie can decay spontaneously to a nucleus of lower mass but differnet combination of nucleons. The process of spontaneous emission of radiation is called radioactivity substance.
Radioactive decay is a statistical process. Radiaactivity is independent of all external conditions. The number of decays per unit time or decay rate is called activity. Activity exponentially decrease with time. Mean lifetime is always greater than half-life time.
Choose the correct statemnet about radioactivity:

Options

A. Radioactivity is a statistical process.
B. Radioactivity is independent of high temperature and high pressure
C. When a nucleus undergoes `alpha`- or - `beta`-decay, its atomic number changes.
D. All of the these

Explanation

To solve the question regarding radioactivity and to choose the correct statement about it, we will analyze each provided statement based on the principles of nuclear physics.

### Step-by-Step Solution:

1. **Understanding Radioactivity**:
- Radioactivity is the spontaneous emission of radiation from unstable nuclei. This process occurs without any external influence and is a statistical phenomenon.

**Hint**: Remember that radioactivity is a natural process that does not require external conditions to occur.

2. **Statistical Nature of Radioactivity**:
- Radioactive decay is indeed a statistical process. This means that while we can predict the average behavior of a large number of nuclei, we cannot predict when a specific nucleus will decay.

**Hint**: Focus on the concept of probability when discussing the decay of individual nuclei versus a large sample.

3. **Independence from External Conditions**:
- Radioactivity is independent of external conditions such as temperature and pressure. This means that changes in these conditions do not affect the rate of decay of radioactive substances.

**Hint**: Consider how temperature and pressure affect chemical reactions but not nuclear processes.

4. **Decay Rate and Activity**:
- The decay rate, also known as activity, is defined as the number of decays per unit time. This activity decreases exponentially over time.

**Hint**: Recall the exponential decay formula and how it relates to half-life and mean lifetime.

5. **Mean Lifetime vs. Half-Life**:
- The mean lifetime of a radioactive substance is the average time that a nucleus exists before decaying, and it is always greater than the half-life. The half-life is the time required for half of the radioactive nuclei in a sample to decay.

**Hint**: Remember the relationship between mean lifetime (τ) and half-life (t₁/₂): τ = t₁/₂ / ln(2).

6. **Changes in Atomic Number**:
- In alpha decay, the atomic number decreases by 2, while in beta decay, the atomic number increases by 1. This means that the type of decay affects the identity of the element.

**Hint**: Visualize the changes in atomic structure during alpha and beta decay to better understand the changes in atomic number.

7. **Conclusion**:
- Based on the analysis, all the statements provided in the question regarding radioactivity are correct. Therefore, the correct answer is "All of the above."

### Final Answer:
The correct statement about radioactivity is: **All of the above**.