Explanation:

Radioactivity:
Radioactivity is the property of certain elements to spontaneously emit radiation. The emission of radiation occurs due to the unstable nature of the atomic nucleus.

Several elements, both natural and artificial, exhibit radioactivity. These elements are often referred to as radioactive elements. Some common examples of naturally occurring radioactive elements include uranium, thorium, and radium.

Types of Radioactive Decay:
Radioactive decay is the process by which an unstable atomic nucleus emits radiation in order to achieve a more stable state. There are three main types of radioactive decay:

1. Alpha Decay: In alpha decay, an atomic nucleus emits an alpha particle, which consists of two protons and two neutrons. This results in the atomic number of the element reducing by 2 and the mass number reducing by 4.

2. Beta Decay: In beta decay, an atomic nucleus emits a beta particle, which can be either an electron (beta-minus decay) or a positron (beta-plus decay). Beta decay occurs when there is an imbalance between the number of protons and neutrons in the nucleus.

3. Gamma Decay: Gamma decay involves the emission of gamma rays, which are high-energy photons. Gamma rays do not cause any change in the atomic number or mass number of the element but are emitted to release excess energy.

Radioactive Isotopes:
Radioactive isotopes are variants of elements that exhibit radioactivity. These isotopes have an unstable atomic nucleus and undergo radioactive decay to achieve stability. For example, uranium-238 is a radioactive isotope of uranium that undergoes alpha decay to form thorium-234.

Applications of Radioactivity:
Radioactivity has various important applications in different fields, including:

1. Medicine: Radioactive isotopes are used in diagnostic imaging techniques like PET scans and in cancer treatment through radiation therapy.

2. Energy Production: Nuclear power plants utilize controlled nuclear reactions to generate electricity.

3. Carbon Dating: Radioactive isotopes like carbon-14 are used to determine the age of archaeological artifacts and fossils.

4. Industrial Applications: Radioactive isotopes can be used as tracers to monitor various industrial processes, such as oil refining and leak detection.

5. Research: Radioactive isotopes are widely used in scientific research to study the behavior of atoms, molecules, and biological systems.

In conclusion, radioactivity is the property of certain elements to emit radiation spontaneously due to the unstable nature of their atomic nuclei. This property has significant applications in various fields and helps us understand the fundamental behavior of matter at the atomic level.