Question

A \(255-\) gram laboratory rat is exposed to \(23.2\) rads. How many grays did the rat receive? How many joules were absorbed by the rat?

Short answer

The rat received 0.232 grays and absorbed approximately 0.05916 joules.

Step-by-step solution

Understanding the Units

First, we need to understand that 1 rad is equal to 0.01 gray (Gy). The gray is the SI unit of absorbed dose and is used to indicate the radiation dose absorbed by a material, where 1 gray equals 1 joule per kilogram.

Convert Rads to Grays

The rat was exposed to 23.2 rads. To find the dose in grays, we convert rads to grays using the conversion factor. \[ \text{Dose in Grays} = 23.2 \, \text{rads} \times 0.01 \, \text{Gy/rad} = 0.232 \, \text{Gy} \]

Calculate Joules Absorbed

To find out how many joules were absorbed by the rat, we use the relation that 1 gray = 1 joule/kg. The rat weighs 255 grams, which converts to 0.255 kg. The energy absorbed in joules is given by multiplying the dose in grays by the mass of the rat in kilograms.\[ \text{Energy absorbed (J)} = 0.232 \, \text{Gy} \times 0.255 \, \text{kg} = 0.05916 \, \text{J} \]

Key concepts

gray (Gy)

The gray (Gy) is an important unit of measurement in the field of radiation. It represents the absorbed dose of radiation energy per unit mass. Specifically, 1 gray is equivalent to the absorption of 1 joule of radiation energy per kilogram of the mass of the object or substance. This unit is part of the International System of Units (SI), which makes it widely used and recognized.
By standardizing radiation doses in grays, scientists and healthcare professionals can accurately compare the effects of radiation exposure across different contexts and materials. This unit helps in assessing the potential biological impacts of radiation on living organisms, as well as its effects on materials and structures.
Converting other units like rad to gray allows for a clearer understanding of the absorbed dose, making it easier to relate to energy absorption and potential biological effects.

rad (radiation absorbed dose)

The rad is another unit of measurement used to quantify radiation exposure and dose. Although older than the gray, it remains in use, particularly in some parts of the world and specific fields. One rad is defined as 0.01 gray (Gy), which means it indicates a smaller measure of radiation absorption compared to gray.
The use of rad becomes particularly handy when discussing lower levels of radiation exposure or in historical contexts, as many older studies and datasets may utilize rad rather than gray. Understanding this unit is crucial for professionals who work with diverse data across different time periods and regions.
In practical applications or scientific measures, converting rad to gray (by multiplying the rad value by 0.01) is often necessary to incorporate this data seamlessly into contemporary assessments and international standards.

joules (energy absorption)

Joules play a critical role as the fundamental units for measuring energy absorption. When it comes to radiation, the absorbed dose is often expressed in terms of energy per unit mass, typically joules per kilogram. This direct relationship facilitates the understanding of how much energy is imparted to a material or organism when it is exposed to radiation.
By converting radiation doses from units like gray or rad into joules, it is easier to present and comprehend the actual energy changes that occur. For example, if a laboratory rat absorbs a certain dose measured in gray, we can determine how much energy has been transferred to the rat's body in joules, which indicates the scale of biochemical changes or potential tissue damage.
This measurement is vital for safety assessments in various industries, including health care, nuclear energy, and scientific research, as it helps to design protocols and protections based on clear energetic changes and thresholds.