Problem 17 - Chemistry: Principles and Reactions

Question

A scintillation counter registers emitted radiation caused by the disintegration of nuclides. If each atom of nuclide emits one count, what is the activity of a sample that registers \(3.00 \times 10^{4}\) disintegrations in five minutes?

Step-by-Step Solution

Answer

Question: Calculate the activity of a sample that has 3.00 x 10^4 disintegrations in 5 minutes. Answer: The activity of the sample is 100 Becquerel (Bq).

Step 1: Convert time from minutes to seconds

Time is given in minutes, so we will first convert it into seconds. 1 minute = 60 seconds 5 minutes = 5 * 60 = 300 seconds. Now that we have the time in seconds, we can proceed to calculate the activity.

Step 2: Calculate activity

The activity (A) can be calculated using the formula: Activity (A) = number of disintegrations (N) / time period (t) Given the number of disintegrations (N = 3.00 x 10^4) and the time period (t = 300 seconds), we can calculate the activity by plugging the values into the formula: A = (3.00 × 10^4) disintegrations / 300 seconds A = (3.00 × 10^4) / 300

Step 3: Calculate the result

Now, we can use a calculator to find the result: A = (3.00 × 10^4) / 300 A = 100 Bq The activity of the sample is 100 Becquerel (Bq).

Key Concepts

Scintillation Counter

A scintillation counter is a device used to detect and measure ionizing radiation. When radiation passes through a certain material inside the counter, this material emits flashes of light, or scintillations. Here's how it works in simple terms:

• Ionizing radiation enters the scintillator material.
• The scintillator absorbs the radiation and emits tiny flashes of light in response.
• These light flashes are detected by a photomultiplier tube, which converts them into an electrical signal.
• The signal is then counted, allowing us to measure the level of radiation.

Scintillation counters are widely used in nuclear chemistry to measure the radiation from disintegrating atoms. They are sensitive and can provide quick results, making them essential tools in both laboratories and medical settings.

Radioactive Disintegration

Radioactive disintegration, also known as radioactive decay, is the process by which unstable atomic nuclei lose energy by emitting radiation. This process involves a transition from a higher energy state to a lower energy state. There are several key points about radioactive disintegration:

• It is a random process, meaning it can't be predicted exactly when a specific atom will disintegrate.
• The disintegration results in the emission of particles like alpha, beta, and gamma radiation.
• Each type of radiation has different properties and penetrative abilities.
• The rate at which a sample decays is called its activity.

Understanding radioactive disintegration is crucial in nuclear chemistry because it helps explain how and why different nuclides emit radiation, which is vital for applications like medical treatments and energy generation.

Activity Calculation

Activity calculation involves determining the decay rate of a radioactive substance. The activity represents how many disintegrations happen in a given time period, typically a second. To calculate this, we use the formula:\[ A = \frac{N}{t} \]Where:

• \( A \) is the activity, measured in disintegrations per second or Becquerel (Bq).
• \( N \) is the total number of disintegrations.
• \( t \) is the time period over which these disintegrations occur.

For example, if a sample undergoes 30,000 disintegrations in 300 seconds, the activity calculates as:\[ A = \frac{30,000}{300} = 100 \text{ Bq} \]This represents that, on average, 100 disintegrations occur per second in the sample. Activity calculations are vital in nuclear chemistry as they allow us to quantify the decay process and assess the sample's radiation output.

Becquerel Unit

The Becquerel (Bq) is a unit used to measure radioactivity. It tells us how many radioactive disintegrations happen each second. Named after Henri Becquerel, who discovered radioactivity, the unit is a cornerstone in understanding nuclear decay. Key characteristics of the Becquerel unit include:

• 1 Becquerel corresponds to 1 disintegration per second.
• It is the internationally accepted unit of radioactivity, replacing the older 'Curie'.
• The use of Bq facilitates accurate measurement and comparison of radioactive samples.

For practitioners and students in nuclear chemistry, understanding the Becquerel unit is fundamental. It's not only about counting disintegrations but also crucial for safety, regulation compliance, and the study of radioactive materials.