A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (b) The rat has a mass of 385 g and is exposed to the radiation for 14.0 s, absorbing 35% of the emitted alpha particles, each having an energy of 9.12 * 10-13 J. Calculate the absorbed dose in millirads and grays.

Verified step by step guidance

1. Convert the activity from millicuries (mCi) to disintegrations per second (becquerels, Bq) using the conversion factor: 1 mCi = 3.7 x 10^7 Bq.
2. Calculate the total number of disintegrations during the exposure time by multiplying the activity in Bq by the exposure time in seconds.
3. Determine the total energy absorbed by the rat by multiplying the total number of disintegrations by the energy per alpha particle and the absorption percentage (35%).
4. Calculate the absorbed dose in grays (Gy) by dividing the total energy absorbed (in joules) by the mass of the rat (in kilograms).
5. Convert the absorbed dose from grays to millirads using the conversion factor: 1 Gy = 100,000 millirads.

Key Concepts

Radioactivity and Alpha Particles

Radioactivity is the process by which unstable atomic nuclei lose energy by emitting radiation. Alpha particles are a type of ionizing radiation consisting of two protons and two neutrons, emitted from the nucleus of an atom. They have a relatively low penetration power but can cause significant damage to biological tissues if absorbed.

Absorbed Dose

The absorbed dose is a measure of the energy deposited by ionizing radiation in a given mass of tissue, expressed in grays (Gy) or rads. One gray is defined as the absorption of one joule of radiation energy per kilogram of matter. The absorbed dose is crucial for assessing the potential biological effects of radiation exposure.

Conversion between Units

In radiation measurement, it is often necessary to convert between different units, such as millirads and grays. One rad is equivalent to 0.01 gray, and one millirad is one-thousandth of a rad. Understanding these conversions is essential for accurately reporting and interpreting radiation doses in various contexts.