Problem 15 - Chemistry: Principles and Reactions

Question

A source for gamma rays has an activity of 3175 Ci. How many disintegrations are there for this source per minute?

Step-by-Step Solution

Answer

Answer: Approximately 7.0485 × 10^14 disintegrations/min.

Step 1: Write down the given activity in curies

The given activity of the gamma-ray source in curies is 3175 Ci.

Step 2: Convert the activity from curies to disintegrations per second using the conversion factor

Using the conversion factor (1 Ci = 3.7 × 10^10 disintegrations per second), let's convert the activity to disintegrations per second: (3175 \, \text{Ci}) \times (3.7 \times 10^{10} \, \text{disintegrations/s})/(\text{Ci}) = 1.17475 \times 10^{13} \, \text{disintegrations/s}.

Step 3: Convert the disintegrations per second to disintegrations per minute

Now, we'll convert from disintegrations per second to disintegrations per minute, knowing that there are 60 seconds in a minute: (1.17475 \times 10^{13} \, \text{disintegrations/s}) \times (60 \, \text{s})/(\text{min}) = 7.0485 \times 10^{14} \, \text{disintegrations/min}.

Step 4: State the final answer

The number of disintegrations for this gamma-ray source per minute is approximately 7.0485 × 10^14 disintegrations/min.

Key Concepts

Gamma Rays

Gamma rays are a form of electromagnetic radiation, similar to X-rays, but with higher energy and shorter wavelength. They are produced during radioactive decay, a process where unstable atomic nuclei release energy to become more stable. Because of their high energy, gamma rays can penetrate materials much deeper than alpha or beta particles. This makes them both useful and dangerous depending on their application.

Gamma rays are often used in:

• Medical treatment, such as cancer radiotherapy, because they can target and destroy unhealthy cells.
• Industrial applications, like examining weld imperfections and thick metal parts.
• Astronomy, to observe cosmic phenomena like supernovae and black holes.

Their ability to penetrate tissues and other materials means that proper shielding, typically using lead or thick concrete, is necessary to protect against exposure.

Activity of Radioactive Sources

The activity of a radioactive source measures how frequently decay events, also known as disintegrations, occur in a radioactive material. It's an indication of how "active" or reactive the material is. Activity is measured in units called becquerels (Bq) or curies (Ci). One curie is a much larger unit than one becquerel and is equivalent to 3.7 x 10^10 disintegrations per second.

Key facts about radioactive activity:

• The higher the activity, the more radiation is being emitted per unit time.
• Over time, as more atoms decay, the activity naturally decreases.
• Activity is crucial in determining safe handling, storage, and disposal methods for radioactive materials.

Understanding the activity helps scientists decide how to apply radioactive materials safely in medicine, industry, and research.

Curie to Disintegrations Conversion

The conversion from curies to disintegrations is essential for understanding the practical effects of radiation from a source. Given that 1 Ci equals 3.7 x 10^10 disintegrations per second, thus to find the total disintegrations per minute, a simple multiplication by 60 is needed, because there are 60 seconds in a minute.

The conversion process involves:

• Identifying the activity in curies.
• Applying the conversion factor to convert from Ci to disintegrations per second: \( ext{Activity in disintegrations per second} = ext{Activity in Ci} imes 3.7 imes 10^{10} \).
• Converting the activity from disintegrations per second to disintegrations per minute by multiplying by 60: \( ext{Activity in disintegrations per minute} = ext{Activity in disintegrations per second} imes 60 \).

Understanding these conversions is crucial for performing and verifying calculations related to the decay processes of radioactive materials accurately.