Question

Tests on human subjects in Boston in 1965 and \(1966,\) following the era of atomic bomb testing, revealed average quantities of about \(2 \mathrm{pCi}\) of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits \(8 \times 10^{-13} \mathrm{~J}\) of energy and if the average person weighs \(75 \mathrm{~kg}\), calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

Short answer

The disintegration rate due to plutonium radioactivity in an average person is \(2 \times 3.7 \times 10^{-2}\) disintegrations/s. The energy deposited in a person's body in a year is \((8 \times 10^{-13} J) \times (2 \times 3.7 \times 10^{-2}) disintegrations/s \times (3.154 \times 10^7) s\). The number of rads in a year is \(\frac{(8 \times 10^{-13} J) \times (2 \times 3.7 \times 10^{-2}) disintegrations/s \times (3.154 \times 10^7) s}{75kg}\), and the number of rems in a year is \(\frac{(8 \times 10^{-13} J) \times (2 \times 3.7 \times 10^{-2}) disintegrations/s \times (3.154 \times 10^7) s}{75kg}\) × 20.

Step-by-step solution

Determine disintegration rate

We are given the level of activity in each person as 2 pCi (picocuries), which is a measure of radioactivity. We know that 1 curie (Ci) is equal to 3.7 × 10^10 disintegrations per second. To convert pCi to Ci, we have: 1 pCi = 10^-12 Ci Thus, we can find the total disintegration rate of plutonium in each person: Disintegration rate = (2 pCi) × (1 Ci / 10^12 pCi) × (3.7 × 10^10 disintegrations/s per Ci) = \(2 \times 3.7 \times 10^{-2} disintegrations/s\)

Calculate energy per year

Now, we will find the total energy deposited in a person's body in a year. We are given that each alpha particle deposits \(8 \times 10^{-13} J\) of energy. There are a total of 2 × 3.7 × 10^(-2) disintegrations per second, and each disintegration results in one alpha particle. Energy per year = (Energy per alpha particle) × (Number of alpha particles per second) × (Number of seconds in a year) = \((8 \times 10^{-13} J) \times (2 \times 3.7 \times 10^{-2}) disintegrations/s \times (3.154 \times 10^7) s\)

Calculate rads

To calculate the number of rads, we need to divide the total energy deposited by the mass of the person in kilograms. We are given that the average person weighs 75 kg. Number of rads = (Energy per year) / (Mass of the person in kg) = \(\frac{(8 \times 10^{-13} J) \times (2 \times 3.7 \times 10^{-2}) disintegrations/s \times (3.154 \times 10^7) s}{75kg}\)

Calculate rems

To calculate the number of rems, we need to multiply the number of rads by the quality factor (QF) of the radiation type. For alpha particles, the QF is 20. Number of rems = (Number of rads) × (Quality Factor) = \(\frac{(8 \times 10^{-13} J) \times (2 \times 3.7 \times 10^{-2}) disintegrations/s \times (3.154 \times 10^7) s}{75kg}\) × 20 Now you have the number of rads and rems of radiation in 1 year from such a level of plutonium in an average person.

Key concepts

Radioactivity

Radioactivity is a natural phenomenon where unstable atomic nuclei release energy in the form of particles or electromagnetic waves. These unstable nuclei reach a more stable state by emitting radiation, which can come in several forms: alpha, beta, and gamma radiation. The process of emission is spontaneous and varies by isotope.

• Alpha particles consist of two protons and two neutrons.
• Beta particles are fast electrons or positrons.
• Gamma rays are high-energy electromagnetic waves.

Understanding radioactivity is crucial, especially because different types of radiation interact differently with materials and living tissue, impacting how we measure and manage radiation exposure.

Plutonium

Plutonium is a radioactive metal with several isotopes. Plutonium- 239 is notable for its use in nuclear weapons and as a fuel in nuclear reactors. Its radioactive decay mainly releases alpha particles.

• Discovered in 1940, plutonium is not naturally abundant.
• It is highly toxic and requires careful handling.
• Plutonium decays via alpha emission, leading to a substantial half-life.

Due to its properties, understanding plutonium is essential for its safe use in energy production and its implications for human health.

Alpha Particles

Alpha particles are large, positively charged particles emitted during radioactive decay. Composed of two protons and two neutrons, they are identical to a helium nucleus.

• Limited penetration ability—can be stopped by a sheet of paper or human skin.
• Highly ionizing when they interact with living tissue.
• Can cause significant damage if ingested or inhaled.

Understanding alpha particles is important for evaluating radiation dosage and protective measures, particularly when handling radioactive substances.

Curie Unit

The Curie (Ci) is a unit of radioactivity that measures the rate at which radioactive atoms decay. Named after Marie Curie, it represents 3.7 × 10^{10} disintegrations per second.

• Curie is used to quantify the intensity of radioactivity.
• 1 Curie is equal to 3.7 × 10^{10} disintegrations/second.
• Smaller units such as the picocurie (pCi) are often used for lower levels of radioactivity.

The Curie is integral in radiation measurement, providing a standard for comparing the activity levels of different radioactive materials.

Radiation Measurement

Radiation measurement involves quantifying the amount of radiation energy being absorbed by a material or biological entity. Understanding these measurements is essential to ensuring safety in both medical and industrial contexts.

• Measuring devices include Geiger counters and scintillation detectors.
• Dosage units like rad and rem aid in assessing the potential danger.
• Precision in measurement helps to mitigate risk and protect health.

Any assessment of exposure risk requires accurate and consistent radiation measurement to ensure protective guidelines are maintained.

Energy Deposition

Energy deposition refers to the transfer of energy from ionizing radiation to the material it passes through. This process causes ionization, resulting in physical or chemical changes.

• Alpha particles deposit energy over short distances.
• Energy deposition can affect biological tissues, leading to cell damage or mutation.
• The amount of energy deposited is critical in determining the effectiveness and danger of the radiation.

Understanding energy deposition is fundamental to calculating safe levels of radiation exposure.

Rad

The rad (radiation absorbed dose) is a unit of absorbed radiation dose, representing the amount of energy deposited in a kilogram of matter.

• 1 rad equals 0.01 joules per kilogram (J/kg).
• Used to describe radiation absorption in biological organisms.
• Essential for understanding potential health effects in exposed tissues.

By quantifying radiation absorption, the rad helps predict biological impacts and establish safety standards for occupational and public exposure.

Rem

The rem (roentgen equivalent man) is an older unit of radiation dosage used to quantify biological effects. It accounts for type of radiation and sensitivity of the affected tissue.

• Incorporates a "quality factor" (QF) that adjusts for different radiation types.
• 1 rem accounts for both energy absorbed and biological effect.
• Commonly used to assess occupational exposure risks.

While the rem has largely been replaced by the sievert in many countries, it remains a crucial concept in understanding radiation protection.

Quality Factor

The Quality Factor (QF) is a dimensionless factor used in radiation protection to account for varying biological effects from different types of radiation. For alpha particles, the QF is particularly important because of their substantial ionizing potential.

• Alpha particles have a QF of 20, indicating a high potential to cause damage compared to other radiation types.
• QF helps convert absorbed doses to biological effective doses.
• Ensures safety standards adjust for different radiation qualities.

Understanding and applying the Quality Factor enhances the accuracy of risk assessments associated with radiation exposure.