Question

A freshly Prepared radioactive source of half life \(2 \mathrm{~h}\) emits radiation of intensity which is 64 times the Permissible safe level. The minimum time after which is would be possible to work safely with this source is. (A) \(6 \mathrm{~h}\) (B) \(24 \mathrm{~h}\) (C) \(12 \mathrm{~h}\) (D) \(36 \mathrm{~h}\)

Short answer

The minimum time after which it would be possible to work safely with this source is 12 hours. So, the correct answer is (C) 12 hours.

Step-by-step solution

Determine number of half-lives required to reach safe level

First, we need to figure out how many times the source must go through its half-life to reduce its intensity to the safe level. The source emits radiation at 64 times the safe level, so we'll need to find the smallest number of half-lives that will multiply by a factor of 1/2 to reduce the intensity to 1 or below.

Calculate the number of half-lives

Starting with the source at 64 times the safe level, consider going through the half-lives: 1st half-life: \(64\cdot\frac{1}{2}=32\) times the safe level. 2nd half-life: \(32\cdot\frac{1}{2}=16\) times the safe level. 3rd half-life: \(16\cdot\frac{1}{2}=8\) times the safe level. 4th half-life: \(8\cdot\frac{1}{2}=4\) times the safe level. 5th half-life: \(4\cdot\frac{1}{2}=2\) times the safe level. 6th half-life: \(2\cdot\frac{1}{2}=1\) time the safe level (finally within the safe level). Thus, the source must go through 6 half-lives to reach the safe level.

Calculate the minimum time for safe work

Now that we know the number of half-lives, we can calculate the time required to reach the safe level. Each half-life is 2 hours long, and this process will take 6 half-lives. Therefore, the total time required to reach the safe level is: Minimum time = Number of half-lives × Half-life time duration Minimum time = 6 × 2 hours = 12 hours The minimum time after which it would be possible to work safely with this source is 12 hours. So, the correct answer is (C) 12 hours.

Key concepts

half-life

The concept of "half-life" is central to understanding how radioactive decay works. The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay or transform into another substance. Each radioactive element has a unique half-life, which can range from fractions of a second to millions of years.
Understanding half-life helps us predict how quickly a radioactive substance will lose its intensity over time. For example, if a substance has a half-life of 2 hours, it means that after 2 hours, its radioactivity will have reduced to half of its original intensity.

• A shorter half-life means that the radioactive decay occurs more rapidly, making the substance less hazardous over a shorter time.
• A longer half-life implies that the substance remains radioactive and potentially hazardous over a more extended period.

In our problem, the source has a half-life of 2 hours, and to reduce the intensity to a safe level (from 64 times above safe) requires multiple half-life periods.

radiation safety

Radiation safety is crucial when dealing with radioactive substances as they emit energy that can be harmful to living organisms. Safe levels ensure that the environment and people are protected from radiation's harmful effects. Radiation exposure is typically measured in levels that are compared against a "permissible safe level."
Exceeding this safe level can lead to potential health risks, including radiation sickness, increased cancer risk, and other health problems. Ensuring radiation safety involves:

• Maintaining exposure levels as low as reasonably achievable (ALARA principle).
• Keeping a safe distance from the radioactive source.
• Using shielding to block or reduce radiation.
• Minimizing the time spent near the source.

In our scenario, the initial radiation was 64 times the permissible level, posing significant risk, and thus required reduction over time to ensure safe conditions.

intensity reduction

Intensity reduction is a key process when dealing with radioactive materials. It refers to decreasing the strength or intensity of radiation emitted over time. This process naturally occurs as the radioactive material decays.
The intensity of a radioactive source diminishes by half with each half-life elapsed. In this exercise, reducing intensity means allowing the radioactive source to decay through a sufficient number of half-lives to reach a level low enough that it aligns with safety protocols.
Let's break down the reduction:

• Starting intensity is 64 times the safe level.
• Each subsequent half-life reduces the intensity by half.

After six half-lives, the intensity reaches 1 time the safe level, making it safe for handling.

time calculation

Time calculation in radioactive decay involves determining how long it will take for a radioactive substance to decay to a desired level of safety. In our exercise, we needed to calculate how many hours it would take for the radioactive intensity to drop from 64 times the safe level to the permissible safe level.
Here's a simple approach to calculate time required:

• Identify how many half-life periods are needed. In our case, 6 half-lives are needed to reduce the intensity to safe levels.
• Calculate the total time by multiplying the number of half-lives by the duration of one half-life.

For the example given, with a half-life of 2 hours, the required time calculation is:\[\text{Total time} = 6 \times 2 \text{ hours} = 12 \text{ hours}\]Thus, it will take 12 hours for the radiation to become safe, showing how time, decay, and safety are intertwined in radioactive management.