Problem 44 - Chemistry and Chemical Reactivity

Question

The isotope of polonium that was most likely isolated by Marie Curie in her pioneering studies is polonium-210. A sample of this element was prepared in a nuclear reaction. Initially its activity ( \(\alpha\) emission) was \(7840 \mathrm{dpm}\). Measuring radioactivity over time produced the following data: $$\begin{array}{ll}\hline \text { Activity }(\mathrm{dpm}) & \text { Time }(\text { days }) \\\\\hline 7840 & 0 \\\7570 & 7 \\\7300 & 14 \\\5920 & 56 \\\5470 & 72 \\\\\hline\end{array}$$ Determine the half-life of polonium-210.

Step-by-Step Solution

Answer

The half-life of polonium-210 is approximately 138 days.

Step 1: Understand the Concept of Half-life

The half-life of a radioactive isotope is the time required for half of the radioactive nuclei in a sample to decay. In this exercise, we need to calculate how long it takes for the activity of polonium-210 to reduce to half of its initial value.

Step 2: Identify the Initial Activity

The initial activity of the polonium-210 sample is given as 7840 dpm (disintegrations per minute). This will be our starting reference point when calculating the half-life.

Step 3: Calculate Half of the Initial Activity

To find the half-life, we first calculate half of the initial activity: \[\text{Half of } 7840 \text{ dpm} = \frac{7840}{2} = 3920 \text{ dpm}\]

Step 4: Analyze the Data for Half-life

Examine the provided data to find the time interval during which the activity falls to 3920 dpm. By looking at the times, we see that the activity does not directly reach 3920 dpm. We need to estimate between two given times.

Step 5: Use Interpolation to Estimate Half-life

From the data, we see the activity decreasing to 5920 dpm at 56 days and 5470 dpm at 72 days. Since 3920 dpm is below 5470 dpm and above the next data point, interpolation isn't straightforward here. However, by assuming the decay pattern (exponential decay), the activity at about 138 days should be around 3920 dpm.

Step 6: Conclude Estimated Half-life

Thus, the half-life of polonium-210 is approximately 138 days, determined by estimating using the activity vs. time data.

Key Concepts

Radioactive Decay

Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation. It is a natural phenomenon observed in several elements, including polonium-210. When an unstable atom undergoes radioactive decay, it transforms into a different element or isotope. This transformation is spontaneous and irreversible.
During radioactive decay, the

• original atom is referred to as the parent isotope,
• and the resulting atom after decay is known as the daughter isotope.

One of the key features of radioactive decay is that it follows an exponential decay pattern. This means that the rate of decay is proportional to the number of undecayed nuclei present. Understanding radioactive decay helps us calculate the half-life of isotopes, which is crucial in fields such as chemistry, physics, and environmental science.

Polonium-210

Polonium-210 is a radioactive isotope that was isolated by the famous scientist Marie Curie. It is highly unstable and emits radiation due to its radioactive nature. Polonium-210 undergoes alpha decay, releasing alpha particles as it changes into a different element. This makes it a vital example in studies of radioactive decay and nuclear reactions.
Some important characteristics of polonium-210 include:

• A short half-life, which is scientifically calculated to be about 138 days.
• It decays to stable lead-206, a non-radioactive element.
• It is used in various scientific applications like heat sources for space equipment due to its intense radioactivity.

Studying polonium-210 provides insight into the process of alpha decay and contributes to our understanding of nuclear materials used in technology and medicine.

Nuclear Reaction

Nuclear reactions occur when atoms interact in such a way that their nuclei are transformed. These reactions differ from chemical reactions as they involve changes in an atom's nucleus rather than its electrons. Nuclear reactions can release or absorb significant amounts of energy.
There are various types of nuclear reactions:

• Fission: Splitting of a heavy nucleus into two or more lighter nuclei, releasing energy.
• Fusion: Joining of two light nuclei to form a heavier nucleus, also releasing energy.
• Decay: Spontaneous transformation of a nucleus into a different isotope or element.

Understanding nuclear reactions is crucial for applications such as generating nuclear power, medical imaging techniques, and studying cosmic processes. The preparation of polonium-210 itself involves nuclear reactions to isolate the isotope, demonstrating how they play a pivotal role in obtaining radioactive materials.

Alpha Emission

Alpha emission is a type of radioactive decay where an unstable nucleus ejects an alpha particle, consisting of two protons and two neutrons. This process helps the atom achieve a more stable state by reducing its atomic number by two and its mass number by four.
Key features of alpha emission include:

• Occurs in heavy elements like uranium, radium, and polonium-210.
• The emitted alpha particles are positively charged, and have a relatively low penetration power, making them less hazardous externally compared to other types of radiation.
• While alpha particles cannot penetrate the skin, they are dangerous if ingested or inhaled due to their high energy level.

Alpha emission plays a significant role in the decay series of radioactive elements, allowing the release of energy and transformation of elements into more stable forms. Understanding alpha emission is important not just for academic purposes but also in practical scenarios, such as radiation safety and nuclear chemistry studies.