Question

Static Charge Static charge can interfere with the production of plastic products by attracting dust and dirt. To reduce it, manufacturers expose the area to polonium-210, which has a half-life of 138 days. How much of a 25.0-g sample will remain after one year (365 days)?

Short answer

After one year (365 days), approximately 6.49 g of the 25.0-g polonium-210 sample will remain.

Step-by-step solution

Determine the number of half-lives that have passed

First, we need to estimate how many half-lives have passed in 365 days. We can calculate this by dividing the total time (365 days) by the half-life (138 days): Number of half-lives = Total time / Half-life

Calculate the remaining quantity of polonium-210

Now, we will use the decay formula to find out how much of the 25.0-g sample will remain after one year. The decay formula is: \(Remaining\ sample\ = Initial\ sample \times (\frac{1}{2})^{number\ of\ half-lives}\) In this case, the initial sample is 25.0 g, and we have calculated the number of half-lives in step 1. By plugging in the values, we can find the remaining sample.

Key concepts

Polonium-210

Polonium-210 is a radioactive isotope of the element polonium. This element is known for its ability to emit alpha particles, which are a type of radiation. These particles are relatively large and can be blocked by materials as thin as a sheet of paper. However, polonium-210 is highly dangerous if ingested or inhaled due to its intense radioactivity.
Polonium-210 is notable because it decays through radioactive decay, specifically alpha decay. This means it loses energy by emitting alpha particles, effectively transforming into a different element altogether. In industrial applications, po-210 is often used to eliminate static charge in environments, such as manufacturing plants producing plastics.

• The element-ejecting alpha particles help in neutralizing static electricity.
• This property makes it invaluable in processes susceptible to static interference.

Half-Life

Half-life is a fundamental concept in understanding radioactive decay. It is the time required for half the atoms in a radioactive sample to decay. This means if you start with a certain amount of a substance, after one half-life, only half of the original amount will remain.
For polonium-210, the half-life is 138 days. This means that every 138 days, the amount of polonium-210 will reduce to half of its previous amount. Understanding half-life helps in predicting how quickly a radioactive substance will decrease over time.
Calculating the number of half-lives that have occurred allows us to use precise mathematical formulas to determine remaining quantities, making half-life an essential tool in many scientific and industrial fields. It’s especially critical in scenarios like managing polonium-210 for static control, ensuring safety and efficiency.

Static Charge

Static charge, or static electricity, occurs when there is an imbalance of electric charges within or on the surface of a material. It can cause various issues, especially in environments dealing with sensitive materials like plastics. This build-up can attract dust and dirt, which affects the quality of the final product.
In manufacturing, static charge must be controlled to ensure high-quality production. Polonium-210 is used as a solution by emitting alpha particles that help neutralize these charges. By interacting with the air and surrounding surfaces, these particles facilitate the loss of static electricity through recombination of electrons and neutralization of ions.

• This reduction of static charge prevents contamination of the products.
• It's a highly effective method in critical industries, enhancing safety and reliability.

Decay Formula

The decay formula is used to calculate how much of a radioactive substance remains after a given period. For polonium-210, the formula involves the initial amount of the substance and the number of half-lives that have passed.
The general decay formula is:\( \text{Remaining sample} = \text{Initial sample} \times \left(\frac{1}{2}\right)^{\text{number of half-lives}} \)This formula allows us to estimate how much of a sample will remain, given the substance's half-life and the elapsed time.
For example, if we start with 25.0 grams of polonium-210 and want to calculate the remaining amount after one year (365 days) given its half-life of 138 days, we first determine how many half-lives have passed. Then, we use the formula to solve:- Determine the number of half-lives: \( 365/138 \approx 2.64 \).
- Calculate the remaining polonium-210 using the decay formula.