Problem 79 - Chemistry The Molecular Science

Question

In June 2009 , researchers at the Joint Institute of Nuclear Research in Dubna, Russia, began continuous bombardment of a \(22-\mathrm{mg}\) target of berkelium- 249 atoms with calcium- 48 nuclei in an attempt to synthesize element 117 . The bombardment continued until January 2010 when evidence indicated that a few atoms of the new element had been synthesized. The half- life of berkelium- 249 is 330 days. Assuming that the reaction period was 240 days, calculate the mass of berkelium-249 remaining.

Step-by-Step Solution

Answer

Approximately 13.13 mg of berkelium-249 remains.

Step 1: Understanding the Half-Life Concept

The half-life of a radioactive substance is the time required for half of the radioactive atoms in a sample to decay. In this problem, berkelium-249 has a half-life of 330 days.

Step 2: Identifying Given Values

We are given the initial mass of berkelium-249, which is 22 mg, the half-life of berkelium-249 as 330 days, and the reaction period as 240 days.

Step 3: Calculating the Number of Half-Lives

Calculate the number of half-lives that have passed. This is done by dividing the total time of the reaction by the half-life:\[\text{Number of half-lives} = \frac{240 \text{ days}}{330 \text{ days/half-life}} \]

Step 4: Calculate the Remaining Berkelium-249

The remaining mass can be calculated using the formula:\[\text{Remaining Mass} = \text{Initial Mass} \times \left(\frac{1}{2}\right)^{\text{Number of half-lives}}\]Substituting the values:\[\text{Remaining Mass} = 22 \text{ mg} \times \left(\frac{1}{2}\right)^{\frac{240}{330}}\]

Step 5: Final Calculations and Conclusion

Proceed with calculating the exponent and then the remaining mass to find the answer.\[\text{Remaining Mass} \approx 22 \times 0.597 = 13.13 \text{ mg}\]Thus, after 240 days, approximately 13.13 mg of berkelium-249 remains.

Key Concepts

Half-Life Calculation

Understanding the concept of half-life is crucial in nuclear chemistry. Half-life is the time it takes for half of a dose of radioactive substance to decay.It essentially measures how quickly a radioactive material transforms into another element or isotope.In our exercise, berkelium-249 has a half-life of 330 days. This means that every 330 days, half of the berkelium-249 atoms will have decayed into something else. This is a key concept when calculating how much of the material remains after a given time.Here's how to calculate the remaining mass of a radioactive substance:

• First, determine how many half-lives have elapsed during the reaction period. You divide the total time period by the half-life of the substance.
• After finding the number of half-lives, use the formula: \(\text{Remaining Mass} = \text{Initial Mass} \times \left(\frac{1}{2}\right)^{\text{Number of half-lives}}\).
• Plug in the numbers to calculate the remaining mass.

These steps help students understand the decay process and make predictions or calculate the amount of a substance left over a period.

Nuclear Chemistry

Nuclear chemistry involves studying chemical processes in which changes in the nucleus of an atom cause transformations from one element to another. This field of chemistry deals not just with radioactive decay, but also with understanding nuclear reactions and their applications. Radioactive decay is one of the fundamental processes studied in nuclear chemistry. It involves particles or electromagnetic waves being emitted from unstable atomic nuclei. These reactions can lead to new element formation, such as what occurred during the synthesis of element 117 in the given exercise. Nuclear chemistry has broad applications:

• Understanding radioactive decay provides insights into aging archaeological artifacts via techniques like carbon dating.
• Nuclear reactions are pivotal in energy production as we see in nuclear power plants.
• Medical imaging and cancer treatment also utilize nuclear chemistry insights.

The study and application of nuclear chemistry facilitate discovering new elements and isotopes, helping scientists further understand the complexities of atomic behavior.

Element Synthesis

Element synthesis is the process by which new chemical elements are created. In the exercise example, scientists tried to synthesize element 117, known today as tennessine. This process is not only fascinating but also a core part of expanding the periodic table. Creating a new element involves colliding atomic nuclei at high energies. This requires both precision and advanced technology, including powerful particle accelerators. Two key aspects of element synthesis to keep in mind:

• Target materials, like berkelium-249, are bombarded with particles such as calcium-48 nuclei to form a new element.
• The resulting element is often unstable, decaying into smaller particles rapidly; thus, it might be detected only for a few moments.

Synthesizing new elements allows scientists to explore unknown territories of chemical properties. Such research can lead to practical applications or deeper knowledge of fundamental atomic interactions. Creating an element outside the known table is an extraordinary achievement of modern science.