Question

What percentage of U-238 radionuclides in a sample remain after two half- lives?

Short answer

After two half-lives, 25% of U-238 radionuclides remain.

Step-by-step solution

Understand the Concept of Half-life

The half-life of a radionuclide is the time it takes for half of the radioactive atoms in a sample to decay. For U-238, if you start with a certain amount, after one half-life, 50% will remain.

First Half-life Calculation

After one half-life, 50% of the original U-238 sample remains. This is because half of the radionuclides have decayed and half remain.

Second Half-life Calculation

After the second half-life, half of the remaining 50% of radionuclides remain. Calculate half of 50%: \[\frac{50}{2} = 25\%\] Thus, after two half-lives, 25% of the original radionuclides remain.

Key concepts

Radioactive Decay

Radioactive decay is a natural process that occurs in unstable atomic nuclei. In this process, the nucleus releases energy by emitting radiation, eventually transforming into a more stable form. This can happen in several ways, such as alpha decay, beta decay, or gamma decay, each involving the release of different particles and energy. The rate at which a radioactive substance decays is consistent and is measured using the concept of half-life.

Key points about radioactive decay include:

• The randomness of decay events, which means we cannot predict exactly when a particular atom will decay, only the statistical rate of decay for a large number of atoms.
• The reduction in radioactivity over time as more atoms decay.
• It is an irreversible process, meaning once a radioactive isotope decays, it cannot return to its original form.

Understanding radioactive decay helps us evaluate the safety and environmental impact of radioactive materials and optimally use them in fields like medicine, archaeology, and energy production.

U-238

U-238, or Uranium-238, is one of the most common isotopes of uranium. It makes up about 99.3% of natural uranium found in the Earth's crust. Though U-238 is not fissile, meaning it cannot sustain a nuclear chain reaction by itself, it can be converted into a fissile isotope, Plutonium-239, in breeder reactors.

Key characteristics of U-238 include:

• U-238 has a very long half-life of approximately 4.5 billion years, which is similar to the age of the Earth.
• It decays via alpha decay, emitting an alpha particle (consisting of two protons and two neutrons) and transforming into Thorium-234.
• Due to its long half-life, U-238 has persisted since the Earth's formation, making it useful for dating geological events.

Thus, U-238 plays a critical role in nuclear science and applications, despite its inability to sustain a chain reaction unaided.

Radionuclides

Radionuclides are atoms with unstable nuclei that emit radiation as they decay into more stable forms. They exist naturally or can be artificially produced in nuclear reactors and accelerators. Radionuclides are key in various scientific and industrial applications due to their unique properties.

Important aspects of radionuclides include:

• They can emit different types of radiation such as alpha particles, beta particles, or gamma rays, depending on the type of decay.
• Each radionuclide has a specific half-life, which is crucial for determining their utility in applications like radiometric dating, medical imaging, and cancer treatment.
• The quantity of radioactivity is measured in units like Becquerels or Curies, reflecting the number of decay events per second.

Radionuclides hold significant value in research and technology, providing insights into the age of objects, treatment of diseases, and the study of atomic interactions.