Passage Problems In \(1972,\) a worker at a nuclear fuel plant in France discovered that uranium from a mine in Oklo, in the African Republic of Gabon, had less U-235 than the normal 0.7 \(\%\) - a quantity known from meteorites and Moon rocks to be constant throughout the solar system. Further analysis showed the presence of isotopes that would result from the decay of fission products. Scientists drew the remarkable conclusion that a natural nuclear fission reaction had occurred some 2 billion years ago, lasting for about 100,000 years. Water, mixing with rich uranium ore, provided the moderator that made the chain reaction possible. More significantly, U-235's 700-million-year half-life means that 2 billion years ago there was a higher abundance of \(U-235\) in natural uranium. At the time of the Oklo fission reaction, the actual amount of U-235 present was a. about the same as today. b. about twice as much as today. c. about four times as much as today. d. about eight times as much as today.

Step by step solution

01

Understanding Half-Life

Half-life is the time required for half of the atoms in a sample of a radioactive isotope to decay. Given that the half-life of U-235 is 700 million years, this means that any quantity of this isotope will be halved every 700 million years.

02

Calculating Number of Half-Lives

In 2 billion years, there will have been 2,000,000,000/700,000,000 = approximately 2.86 half-lives of U-235.

03

Determining Initial Quantity

After one half-life, the quantity of U-235 would have been twice what it is today; after two half-lives, it would have been four times; and after three half-lives, it would have been eight times. As 2.86 half-lives falls between two and three half-lives, the amount of U-235 present at the time of the Oklo reaction would have been between four and eight times the current amount. Therefore, the answer that is closest, yet not overestimating, is four times as much as today.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Half-Life of U-235

Radioactive substances undergo a process called decay, where they break down into more stable atoms over time. One crucial aspect in understanding this process is the concept of 'half-life'. The half-life of a radioactive isotope, like Uranium-235 (U-235), is defined as the time it takes for half of the atoms in a given sample to decay.

For U-235, this half-life is approximately 700 million years. In simpler terms, if you have a sample of U-235, after 700 million years, you would expect to have half the amount of U-235 you started with. This concept is foundational in determining the age of ancient materials and understanding the behavior of radioactive substances over time.

In terms of the exercise problem, this half-life allows us to work out how much U-235 would have been present in the past. By knowing the current half-life and considering that no external sources have altered the decay rate, we can back-calculate to find out how abundant U-235 was at any given time in history.

The Process of Uranium Decay

Uranium decay is a natural occurrence with considerable implications for both science and technology. Uranium, prominently U-235, is a heavy metal with a unique capability to undergo fission, splitting into smaller nuclei along with a release of energy.

This decay process involves the transformation of U-235 to lead over several intermediate radioactive decay steps, known as decay chains. These steps are characterized by a variety of emissions, including alpha (α) particles, beta (β) particles, and in some cases, gamma (γ) rays.

The rate at which U-235 decays into its daughter isotopes is governed by its half-life. Nuclear engineers and geologists utilize the concept of half-life and decay chains to understand energy production in nuclear reactors and perform radiometric dating to estimate the age of rocks.

The Oklo Phenomenon

The Oklo phenomenon is an awe-inspiring natural occurrence that illustrates how a nuclear fission reaction can happen in nature. Discovered in the 1970s in Oklo, Gabon, this natural nuclear reactor formed about 2 billion years ago.

At that time, the concentration of U-235 in uranium ore was much higher, allowing for a sustained nuclear chain reaction. The conditions in Oklo were just right: there was a high concentration of uranium along with groundwater which acted as a moderating agent to slow down neutrons and promote the fission of U-235.

The Oklo phenomenon is the only known instance on Earth where such natural conditions led to a self-sustained nuclear reaction, which lasted for hundreds of thousands of years. This event not only highlights the unique conditions of Earth's geologic past but also provides an invaluable natural laboratory to study the processes, by-products, and remnants of nuclear fission outside of a man-made reactor.