11.3 Units of Radioactivity

Learning Objective

  1. Express amounts of radioactivity in a variety of units.

In Section 11.2 "Half-Life", we used mass to indicate the amount of radioactive substance present. This is only one of several units used to express amounts of radiation. Some units describe the number of radioactive events occurring per unit time, while others express the amount of a person’s exposure to radiation.

Perhaps the direct way of reporting radioactivity is the number of radioactive decays per second. One decay per second is called one becquerel (Bq)A unit of radioactivity equal to one decay per second.. Even in a small mass of radioactive material, however, there are many thousands of decays or disintegrations per second. The unit curie (Ci)A unit of radioactivity equal to 3.7 × 1010 decays per second., now defined as 3.7 × 1010 decays per second, was originally defined as the number of decays per second in 1 g of radium. Many radioactive samples have activities that are on the order of microcuries (µCi) or more. Both the becquerel and curie can be used in place of grams to describe quantities of radioactive material. As an example, the amount of americium in an average smoke detector has an activity of 0.9 µCi.


The unit becquerel is named after Henri Becquerel, who discovered radioactivity in 1896. The unit curie is named after Polish scientist Marie Curie, who performed some of the initial investigations into radioactive phenomena in the early 1900s.

Example 4

A sample of radium has an activity of 16.0 mCi (millicuries). If the half-life of radium is 1,600 y, how long before the sample’s activity is 1.0 mCi?


The following table shows the activity of the radium sample over multiple half-lives:

Time in Years Activity
0 16.0 mCi
1,600 8.0 mCi
3,200 4.0 mCi
4,800 2.0 mCi
6,400 1.0 mCi

Over a period of 4 half-lives, the activity of the radium will be halved four times, at which point its activity will be 1.0 mCi. Thus, it takes 4 half-lives, or 4 × 1,600 y = 6,400 y, for the activity to decrease to 1.0 mCi.

Skill-Building Exercise

  1. A sample of radon has an activity of 60,000 Bq. If the half-life of radon is 15 h, how long before the sample’s activity is 3,750 Bq?

Other measures of radioactivity are based on the effects it has on living tissue. Radioactivity can transfer energy to tissues in two ways: through the kinetic energy of the particles hitting the tissue and through the electromagnetic energy of the gamma rays being absorbed by the tissue. Either way, the transferred energy—like thermal energy from boiling water—can damage the tissue.

The radA unit of radioactive exposure equal to 0.01 J/g of tissue. (an acronym for radiation absorbed dose) is a unit equivalent to a gram of tissue absorbing 0.01 J:

1 rad = 0.01 J/g

Another unit of radiation absorption is the gray (Gy):

1 Gy = 100 rad

The rad is more common. To get an idea of the amount of energy this represents, consider that the absorption of 1 rad by 70,000 g of H2O (approximately the same mass as a 150 lb person) would increase its temperature by only 0.002°C. This may not seem like a lot, but it is enough energy to break about 1 × 1021 molecular C–C bonds in a person’s body. That amount of damage would not be desirable.

Predicting the effects of radiation is complicated by the fact that various tissues are affected differently by different types of emissions. To quantify these effects, the unit remA unit of radioactive exposure that includes a factor to account for the type of radioactivity. (an acronym for roentgen equivalent, man) is defined as

rem = rad × factor

where factor is a number greater than or equal to 1 that takes into account the type of radioactive emission and sometimes the type of tissue being exposed. For beta particles, the factor equals 1. For alpha particles striking most tissues, the factor is 10, but for eye tissue, the factor is 30. Most radioactive emissions that people are exposed to are on the order of a few dozen millirems (mrem) or less; a medical X ray is about 20 mrem. A sievert (Sv) is a related unit and is defined as 100 rem.

What is a person’s annual exposure to radioactivity and radiation? Table 11.3 "Average Annual Radiation Exposure (Approximate)" lists the sources and annual amounts of radiation exposure. It may surprise you to learn that fully 82% of the radioactivity and radiation exposure we receive is from natural sources—sources we cannot avoid. Fully 10% of the exposure comes from our own bodies—largely from 14C and 40K.

Table 11.3 Average Annual Radiation Exposure (Approximate)

Source Amount (mrem)
radon gas 200
medical sources 53
radioactive atoms in the body naturally 39
terrestrial sources 28
cosmic sources 28
consumer products 10
nuclear energy 0.05
Total 358


Flying from New York City to San Francisco adds 5 mrem to your overall radiation exposure because the plane flies above much of the atmosphere, which protects us from most cosmic radiation.

The actual effects of radioactivity and radiation exposure on a person’s health depend on the type of radioactivity, the length of exposure, and the tissues exposed. Table 11.4 "Effects of Short-Term Exposure to Radioactivity and Radiation" lists the potential threats to health at various amounts of exposure over short periods of time (hours or days).

Table 11.4 Effects of Short-Term Exposure to Radioactivity and Radiation

Exposure (rem) Effect
1 (over a full year) no detectable effect
∼20 increased risk of some cancers
∼100 damage to bone marrow and other tissues; possible internal bleeding; decrease in white blood cell count
200–300 visible “burns” on skin, nausea, vomiting, and fatigue
>300 loss of white blood cells; hair loss
∼600 death

One of the simplest ways of detecting radioactivity is by using a piece of photographic film embedded in a badge or a pen. On a regular basis, the film is developed and checked for exposure. A comparison of the exposure level of the film with a set of standard exposures indicates the amount of radiation a person was exposed to.

Another means of detecting radioactivity is an electrical device called a Geiger counterAn electrical device that detects radioactivity. (Figure 11.2 "Detecting Radioactivity"). It contains a gas-filled chamber with a thin membrane on one end that allows radiation emitted from radioactive nuclei to enter the chamber and knock electrons off atoms of gas (usually argon). The presence of electrons and positively charged ions causes a small current, which is detected by the Geiger counter and converted to a signal on a meter or, commonly, an audio circuit to produce an audible “click.”

Concept Review Exercise

  1. What units are used to quantify radioactivity?


  1. the curie, the becquerel, the rad, the gray, the sievert, and the rem

Key Takeaway

  • Radioactivity can be expressed in a variety of units, including rems, rads, and curies.


  1. Define rad.

  2. Define rem.

  3. How does a becquerel differ from a curie?

  4. How is the curie defined?

  5. A sample of radon gas has an activity of 140.0 mCi. If the half-life of radon is 1,500 y, how long before the activity of the sample is 8.75 mCi?

  6. A sample of curium has an activity of 1,600 Bq. If the half-life of curium is 24.0 s, how long before its activity is 25.0 Bq?

  7. If a radioactive sample has an activity of 65 µCi, how many disintegrations per second are occurring?

  8. If a radioactive sample has an activity of 7.55 × 105 Bq, how many disintegrations per second are occurring?

  9. Describe how a radiation exposure in rems is determined.

  10. Which contributes more to the rems of exposure—alpha or beta particles? Why?

  11. Use Table 11.4 "Effects of Short-Term Exposure to Radioactivity and Radiation" to determine which sources of radiation exposure are inescapable and which can be avoided. What percentage of radiation is unavoidable?

  12. What percentage of the approximate annual radiation exposure comes from radioactive atoms that are in the body naturally?

  13. Explain how a film badge works to detect radiation.

  14. Explain how a Geiger counter works to detect radiation.


  1. Known as the radiation absorbed dose, a rad is the absorption of 0.01 J/g of tissue.

  2. A becquerel is smaller and equals 1 decay per second. A curie is 3.7 × 1010 Bq.

  3. 6000 y

  4. 2.41 × 106 disintegrations per second

  5. The radiation exposure is determined by the number of rads times the quality factor of the radiation.

  6. At least 16% (terrestrial and cosmic sources) of radioactivity is unavoidable; the rest depends on what else a person is exposed to.

  7. A film badge uses film, which is exposed as it is subjected to radiation.