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Radioactive Decay Law Quiz
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Radioactive Decay Law Quiz

Created by
@PleasantPromethium

Questions and Answers

What is the primary reason for using technetium-99m in medical diagnostics?

  • It has a long half-life.
  • It emits high levels of gamma rays.
  • It does not remain radioactive for very long. (correct)
  • It is the only radioisotope available for imaging.

    • Which of the following medical imaging applications does technetium-99m NOT typically address?

  • Liver imaging
  • Thyroid imaging
  • Bone marrow imaging
  • Genetic testing (correct)

    • What happens to technetium-99m after it undergoes gamma decay?

  • It forms stable technetium-98.
  • It decays into molybdenum-99.
  • It forms ground-state technetium-99. (correct)
  • It remains unchanged.

    • What is the half-life of technetium-99m?

    <p>6 hours</p> Signup and view all the answers

    At temperatures below 7.46 K, what unique property does pure metallic technetium exhibit?

    <p>It exhibits superconductivity.</p> Signup and view all the answers

    Which element does technetium-99 decay into after a series of transformations?

    <p>Ruthenium (element 44)</p> Signup and view all the answers

    What is the decay process of technetium-99m primarily responsible for?

    <p>Emitting gamma rays.</p> Signup and view all the answers

    Which of the following describes the relationship between decay constant and half-life?

    <p>Half-life decreases as decay constant increases.</p> Signup and view all the answers

    What is the Linear Attenuation Coefficient for 200 keV gamma-rays in aluminium?

    <p>0.46 cm⁻¹</p> Signup and view all the answers

    Which of the following statements regarding radiation protection is true?

    <p>Higher atomic number materials are more effective at attenuating gamma-rays.</p> Signup and view all the answers

    What is the SI unit of absorbed dose?

    <p>Gray</p> Signup and view all the answers

    How many half-thicknesses of absorber are needed to reduce gamma-ray intensity by a factor of 8?

    <p>3</p> Signup and view all the answers

    Which radionuclide has the shortest half-life?

    <p>Tritium</p> Signup and view all the answers

    Why are alpha and beta emitters considered more hazardous when ingested?

    <p>They interact more effectively with body tissues.</p> Signup and view all the answers

    What thickness of aluminium is required to reduce gamma-rays by a factor of ten?

    <p>7 cm</p> Signup and view all the answers

    How is the quantity called when energy is deposited in the absorber during radiation interaction?

    <p>Absorbed Dose</p> Signup and view all the answers

    What does the decay constant (λ) signify in the radioactive decay law?

    <p>The rate of decay of radioactive nuclei based on nuclear properties</p> Signup and view all the answers

    Which of the following correctly describes the relationship represented by the radioactive decay law equation?

    <p>Nt decreases in an exponential fashion with time</p> Signup and view all the answers

    What is the relationship between the Decay Constant and Half Life as indicated in the equation?

    <p>$ ext{Decay Constant} = rac{0.693}{ ext{Half Life}}$</p> Signup and view all the answers

    What happens to the curve representing radioactive decay when the decay constant has a high value?

    <p>The curve decreases quickly over time</p> Signup and view all the answers

    How long will it take for 1/16th of the radioisotope 99mTc to remain?

    <p>24 hours</p> Signup and view all the answers

    What does the half-life of a radioisotope represent?

    <p>The time it takes for the activity to decrease by a factor of two</p> Signup and view all the answers

    What does the term 'Half Value Layer' refer to in the context of radiation intensity?

    <p>The thickness of material required to reduce intensity by half</p> Signup and view all the answers

    The natural logarithm in the expression of the radioactive decay law is used to transform what kind of relationship?

    <p>An exponential decay relationship into a linear form</p> Signup and view all the answers

    Which mathematical model describes the relationship between the intensity of radiation and its absorber thickness?

    <p>Exponential Attenuation Model</p> Signup and view all the answers

    What is indicated by the Linear Attenuation Coefficient (μ) in radiation physics?

    <p>The rate at which radiation intensity decreases</p> Signup and view all the answers

    Which of the following statements about nuclear decay is correct?

    <p>The decay constant impacts how quickly a nucleus decays</p> Signup and view all the answers

    What type of mathematical function describes the decay of radioactive nuclei over time?

    <p>Exponential function with negative growth</p> Signup and view all the answers

    If a material reduces radiation intensity to 10% of its original value, how does it relate to the Half Value Layer?

    <p>It is equal to two Half Value Layers</p> Signup and view all the answers

    Which equation represents the decay process of materials over time in radioactive decay?

    <p>$I_x = I_0 e^{- ext{Decay Constant} imes t}$</p> Signup and view all the answers

    The integration of the radioactive decay equation leads to which final expression?

    <p>Nt = N0 * exp(-λt)</p> Signup and view all the answers

    How much aluminum is necessary to reduce the intensity of a 200 keV gamma-ray beam to 10% of its original intensity?

    <p>4.5 cm</p> Signup and view all the answers

    What does 1 Gy correspond to in rad?

    <p>100 rad</p> Signup and view all the answers

    Which unit is used to measure the activity of radioactive materials?

    <p>Curie (Ci)</p> Signup and view all the answers

    What is the relationship between Becquerel and disintegrations per second?

    <p>1 Bq = 1 disintegration per second</p> Signup and view all the answers

    Which of the following correctly describes the concept of half-life?

    <p>The time taken for half the nuclei in a sample to decay</p> Signup and view all the answers

    If a sample has an activity of 1 Ci, what is its equivalent in Becquerel?

    <p>3.7 x 10^10 Bq</p> Signup and view all the answers

    What range of effective dose (mSv) is typical for a mammogram?

    <p>0.04 mSv</p> Signup and view all the answers

    What term describes the factor that accounts for the biological effectiveness of different types of radiation?

    <p>Quality factor</p> Signup and view all the answers

    Which isotope has the shortest half-life among the following options?

    <p>I-131</p> Signup and view all the answers

    How is the dose-equivalent (DE) in sieverts calculated?

    <p>By multiplying dose in Gy by the quality factor</p> Signup and view all the answers

    What is the activity level of a kilobecquerel (kBq) in disintegrations per second?

    <p>1,000 Bq</p> Signup and view all the answers

    Study Notes

    Radioactive Decay Law

    • Radioactive decay is represented mathematically as ( N_t = N_0 \cdot \exp(-\lambda t) ).
    • ( N_0 ) is the initial number of radioactive nuclei, ( N_t ) is the quantity at time ( t ), and ( \lambda ) is the decay constant (in s(^{-1})).
    • Decay occurs exponentially, with the rate determined by the decay constant, a unique property of the radioactive isotope.
    • The number of decaying nuclei over a time interval is proportional to both the current amount of nuclei ( N ) and the time interval ( dt ).
    • Integration of the decay equation yields the Radioactive Decay Law, which can be visualized with a graph showing exponential decline.

    Half-Life

    • Half-life is the duration required for the quantity of a radioisotope to reduce by half.
    • Radioisotopes with short half-lives are ideal for medical diagnostics, resulting in lower radiation exposure.
    • Technetium-99 (99mTc) has a half-life of 6 hours, decaying to stable ruthenium-99 and emitting beta particles without gamma rays.
    • Technetium-99m is widely used in diagnostic imaging of various organs and has a rapid turnover in the human body.

    Decay Constant and Half-Life Relationship

    • The relationship between the decay constant ( \lambda ) and half-life ( t_{1/2} ) is given by ( \lambda = \frac{0.693}{t_{1/2}} ).
    • For 99mTc, it takes 24 hours for the radioactivity to reduce to 1/16th of its original amount, verified through calculations.

    Mathematical Model of Attenuation

    • Radiation intensity is described by the equation ( I_x = I_0 \cdot \exp(-\mu x) ), where ( I_x ) is the intensity after passing through an absorber of thickness ( x ) and ( \mu ) is the linear attenuation coefficient.
    • Half Value Layer (HVL) indicates the thickness of the absorbing material needed to halve the radiation intensity.

    Calculations for Absorbing Material

    • To reduce the intensity of a 200 keV gamma-ray beam to 10%, approximately 7 cm of aluminum is required based on the HVL of 2.14 cm.
    • Aluminium's limited effectiveness as a radiation shield highlights the need for materials with higher atomic numbers for better gamma-ray attenuation.

    Units of Measurement

    • Radioactive decay activity is measured in becquerels (Bq), with 1 Bq equaling 1 disintegration per second. Larger units include kBq, MBq, GBq, and TBq.
    • Curie (Ci) is an older unit, equivalent to ( 3.7 \times 10^{10} ) Bq.
    • Radiation doses are measured in gray (Gy) for absorbed dose and sievert (Sv) for dose equivalent.

    Effective Dose from Radiological Procedures

    • Average effective doses for various diagnostic procedures range from 0.01 mSv for dental x-rays to 8.0 mSv for abdominal CT scans.
    • Understanding these doses helps in assessing the risk and benefits of medical imaging techniques.

    Radioactive Isotope Examples with Half-Lives

    • Tritium: 12.4 years
    • Carbon-14: 5730 years
    • Sulphur-35: 87.4 days
    • Phosphorus-32: 14.3 days
    • Iodine-125: 60.1 days

    Radiation Hazards

    • Alpha and beta emitters pose higher risks when ingested or inhaled, while neutrons, x-rays, and gamma rays are especially hazardous to the entire body.
    • Effective radiation protection often employs materials like lead, concrete, or water to reduce intensity.

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    Description

    Test your knowledge on the radioactive decay law and its mathematical representation. This quiz covers the concepts of initial radioactive nuclei, decay constant, and how the number of nuclei decreases over time. Understand the exponential nature of decay and its implications in nuclear physics.

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