HALF LIFE Comprehensive Study Notes on Radioactivity, Half-Life Calculations, Isotopes Applications, and Safety Precautions

Meaning and Nature of Half-Life

• Decrease in Radiation Intensity Over Time:
  • Any source of radiation gets weaker as time goes on, and the intensity of radiation produced becomes smaller.
  • Physical Mechanism: The number of unstable (radioactive) nuclides (nuclei) decreases as they decay into more stable forms.

• Definitions of Half-Life:
  • Definition 1: It is the time taken for the activity of the source to be reduced to half its original value.
  • Definition 2: It is the average time for half the number of atoms to decay.

Decay Curves and Half-Life Calculations

• Example 1: Calculating Required Duration for Activity Decay:
  • Question: A radioactive sample has a half-life of $3\,\text{hours}$ and an initial activity of $720\,\text{count/min}$. When will the activity be $45\,\text{count/min}$?
  • Step-by-Step Calculation:
  • Start ($t = 0\,\text{hours}$): $720\,\text{count/min}$
  • After 1st half-life ($t = 3\,\text{hours}$): $\frac{720}{2} = 360\,\text{count/min}$
  • After 2nd half-life ($t = 6\,\text{hours}$): $\frac{360}{2} = 180\,\text{count/min}$
  • After 3rd half-life ($t = 9\,\text{hours}$): $\frac{180}{2} = 90\,\text{count/min}$
  • After 4th half-life ($t = 12\,\text{hours}$): $\frac{90}{2} = 45\,\text{count/min}$
  • Conclusion: 4 half-lives are required. Since each half-life is $3\,\text{hours}$, a total time of $4 \times 3\,\text{hours} = 12\,\text{hours}$ is needed.

• Example 3: Finding Half-Life from Experimental Data Table:

  • Table Data:
  • Time ($\text{hours}$): $0$, $5$, $10$, $15$, $20$, $25$
  • Activity ($\text{count/min}$): $500$, $402$, $253$, $180$, $124$, $90$
  • Analysis:
  • Initial activity ($t = 0\,\text{hours}$) = $500\,\text{count/min}$.
  • Half of initial activity = $250\,\text{count/min}$.
  • The activity drops to $253\,\text{count/min}$ (approximately $250\,\text{count/min}$) after $10\,\text{hours}$. This means the half-life of the sample is $10\,\text{hours}$.
  • Note that after $10\,\text{hours}$ more (after $20\,\text{hours}$ from the start), the activity is reduced to $124\,\text{count/min}$ (which is nearly half of $250\,\text{count/min}$).

• Example 4: Finding Half-Life from Decay Curve:

  • Graph Analysis:
  • Initial activity at $t = 0\,\text{days}$ = $400\,\text{count/min}$.
  • Half of initial activity = $200\,\text{count/min}$.
  • The activity reaches $200\,\text{count/min}$ (half of original value) after $4\,\text{days}$. Therefore, Half-life = $4\,\text{days}$.
  • Note that after $4\,\text{days}$ more ($t = 8\,\text{days}$), the activity is reduced to $100\,\text{count/min}$ (half of $200\,\text{count/min}$). Every $4\,\text{days}$, the activity of the sample is reduced by half.

Applications and Uses of Radioactive Isotopes

• Use 1: Detecting Thickness of Paper:
  • Procedure: Paper is rolled and passed continuously between a beta source and a detector.
  • Detection Principle:
  • If paper thickness is uniform, the detector reading remains nearly constant.
  • When reading decreases, this indicates a thicker part of the paper because absorption of radiation by paper increases.
  • Thinner parts allow more radiation through and give a higher count rate.
  • Choice of Source Type:
  • A beta source is used in this application (not alpha or gamma).
  • Alpha is unsuitable because alpha particles will not even penetrate the paper.
  • Gamma is unsuitable because gamma rays are highly penetrative, meaning minor thickness variations are not detected.
  • Half-Life Requirement: A source with a long half-life is needed so that emission activity remains nearly constant over time.

• Use 2: Tracing Applications:
  • Tracers in Medicine:
  • Clinical Uses: Used to detect brain tumors and internal bleeding.
  • Method: A radioactive source is injected or swallowed.
  • Monitoring: The source is traced by a detector or other imaging devices. A high count rate shows good flow of the isotope in blood.
  • Source Requirements:
    • Must be a gamma emitter.
    • Reason 1: Alpha and beta particles have low penetration power, making them hard to detect from outside the body.
    • Reason 2: Alpha and beta particles cause greater cell damage due to their higher ionization power.
    • Must have a short half-life so that it decays quickly to avoid side effects.

• Tracers in Agriculture:
  • Method: A radioactive source is added to irrigation water.
  • Monitoring: The source is traced through the plant system by a detector or other devices.

• Tracers in Industry (Leaks of Pipes):
  • Method: A radioactive source is added to water flowing inside the pipe.
  • Monitoring: The source is traced along the ground above the pipe route using a detector. A leak creates a concentrated pool of radioactive liquid, producing a high count rate on the detector above the leak.

• Use 3: Radiotherapy:

  • Cancer Treatment: Gamma rays emitted from a strong Cobalt-60 ($^{60}\text{Co}$) radioisotope are used in the medical treatment of cancer.

• Use 4: Sterilization:

  • Medical Instruments: Gamma rays are used to sterilize medical instruments by killing bacteria.
  • Food Preservation: Gamma rays are used to irradiate certain foods, killing bacteria to preserve food for longer periods.
  • Food Safety: Irradiated foods are safe to use as no radioactive material goes into the food.
  • Precautions: The exposure dose has to be chosen with care because long exposure to radiation can be dangerous.

• Use 5: Smoke Detector:

  • Applications: Frequently installed in domestic kitchens, and in public buildings such as offices and hotels.
  • Radioisotope Source: Uses Americium-241 ($^{241}\text{Am}$), which is a source of alpha ($\alpha$) radiation.
  • Half-Life: The Americium source used in smoke detectors has a long half-life of about $430\,\text{years}$.
  • Operational Mechanism:
  • Radiation from the source falls continuously on a detector.
  • Since alpha radiation consists of charged particles, a small current flows in the detector.
  • When smoke enters the gap between the source and detector, it absorbs the alpha radiation, preventing alpha radiation from reaching the detector.
  • When the detector stops detecting alpha particles, an alarm sounds.
  • Reason for Choosing Alpha Radiation: A source of alpha radiation is chosen because alpha radiation is easily absorbed by smoke particles.

Dangers, Biological Harms, and Radiation Safety Precautions

• Industrial Safety and Disposal Procedures:
  • Industrial Handling: Industrial sources are held using long tongs and transported in thick lead containers.
  • Radioactive Waste Disposal: Waste radioactive products are enclosed in steel containers and then buried deep in concrete bunkers.

• Dangers and Safety in School Labs:

  • Avoid Contamination: Food should not be taken near radioactive sources to avoid possible contamination.
  • Washing: Always wash hands after any use of radioactive sources.
  • Handling Tools: Always lift radioactive sources with forceps or long tongs.
  • Eye Protection: Sources must never be held near the eyes.
  • Proper Storage: Sources must be kept in their designated storage boxes when not in use.
  • Warning Labels: Sources and containers should display the standard warning label for radiation.
  • Protective Clothing: Gloves should be worn when handling sources, and a lead coat/apron should be worn for body safety.

• Specific Harms of Radioactivity:

  1. Radiation Burns: Beta and gamma radiation can cause radiation burns (i.e. redness and sores on the skin).
  2. Leukemia: Blood cancer caused by radiation damage to bone marrow.
  3. Eye Cataracts: Exposure to radiation can cause cataracts leading to blindness.
  4. Cancer and Sterility: Induces malignant growth and reproductive damage resulting in sterility.
  5. Mutations: Ionizing radiation can cause DNA and cell mutation.