Half-life and radioactive decay

Introduction to radioactive decay

Radioactive decay is a natural process through which unstable atomic nuclei lose energy. This energy is released as radiation. Unstable isotopes, called radioisotopes, will change into more stable isotopes over time. This change occurs because the nucleus of a radioactive atom releases particles and electromagnetic waves, resulting in a transformation into a different element or a different isotope of the same element.

Understanding half-life

The concept of half-life is a way of measuring the rate of decay of radioactive isotopes. The half-life of a radioactive substance is defined as the time it takes for half of the radioactive atoms in a sample to decay.

For example, if you have a sample with 1000 radioactive atoms and the half-life of the element is 2 years, it will take 2 years for 500 atoms to decay, leaving only 500 atoms. After another 2 years, 250 of those atoms will decay, leaving 250 atoms, and so on.

Example: carbon-14

Carbon-14 is a radioactive isotope of carbon that is commonly used in dating archaeological finds. Carbon-14 has a half-life of about 5730 years. This means that if you have a sample of organic material, after 5730 years, only half of the original carbon-14 content will be left in the sample. Knowing the amount of carbon-14 remaining helps scientists estimate the age of objects.

Exponential nature of radioactive decay

The decay of radioactive atoms is an exponential process, meaning that instead of decreasing by a fixed amount each year, the number of atoms decreases by a consistent percentage. Therefore, the largest decline on a percentage basis occurs in the first time period, and later, smaller absolute numbers of atoms continue to decay over the same time interval.

Formula: N(t) = N₀ * (1/2)^(t/T)
    

N(t) is the remaining amount of the substance at time t, N₀ is the initial amount of the substance, and T represents the half-life of the substance.

Example calculation

Suppose you start with a 10-gram sample of a radioactive isotope that has a half-life of 5 years. How much of the isotope will be left after 15 years?

n(15) = 10 * (1/2)^(15/5)
      = 10 * (1/2)^3
      = 10 * 1/8
      = 1.25 grams
    

Types of radioactive decay

Alpha decay

In alpha decay, the nucleus emits an alpha particle, which consists of two protons and two neutrons. This reduces the mass of the original nucleus, causing it to decay into a different element. For example, uranium-238 decays into thorium-234 through the emission of an alpha particle.

Beta decay

Beta decay occurs when a neutron in the nucleus turns into a proton and emits an electron (beta particle) and an antineutrino. In beta decay, the atomic number of the element increases by one, while the mass number remains the same. For example, carbon-14 decays into nitrogen-14 via beta decay.

Gamma decay

Gamma decay involves the emission of gamma rays. These are high-energy electromagnetic waves emitted from the nucleus. Gamma decay often occurs after alpha or beta decay, as the nucleus moves to a lower energy state.

Modern applications of radioactive decay

Carbon dating

As mentioned earlier, carbon-14 dating is a popular method for dating ancient organic material. By measuring how much carbon-14 is left in a sample, researchers can estimate when the organism died.

Medical uses

Radioactive isotopes are used in many ways in medicine. For example, iodine-131 is used in the treatment of thyroid disorders, and technetium-99m is commonly used in imaging procedures such as SPECT scans to diagnose problems in the bones, heart, and other organs.

Energy production

Nuclear power plants use radioactive decay to produce energy. The process uses uranium or plutonium isotopes that undergo fission — a different type of nuclear reaction than decay — to produce heat and generate electricity.

Conclusion

Understanding the nature of half-life and radioactive decay provides important insights into the transformation of matter over time. These concepts not only play a vital role in scientific research and technology, but also offer real-world applications in fields such as archaeology, medicine, and energy production. By exploring the fundamental principles of nuclear physics, learners can appreciate the complex balance of matter and the constant changes that occur in the natural world.

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