Calculate the distance an experimenter must remain from a 3 Ci Ra-226 source at 1 cm to not receive more than 0.1 mCi in a week.

Calculate the distance an experimenter must remain from a 3 Ci Ra-226 source at 1 cm to not receive more than 0.1 mCi in a week.

• A. Approximately 1.7 centimeters
• B. Approximately 17 centimeters
• C. Approximately 0.17 meters
• D. Approximately 1.7 meters

Answer: (D)

The distance needed follows the inverse-square law: exposure rate from a point source is proportional to the activity divided by the square of the distance (rate ∝ A / r^2). Convert the limit to the same units as the source: 0.1 mCi = 0.0001 Ci. At 1 cm from a 3 Ci source, the rate is proportional to 3 Ci / (1 cm)^2. At distance r (in cm), the rate is 3 / r^2 Ci per unit time. Set this equal to the allowed weekly rate: 3 / r^2 = 0.0001 r^2 = 3 / 0.0001 = 30000, so r = sqrt(30000) ≈ 173 cm ≈ 1.73 m. Therefore, about 1.7 meters are needed to keep exposure at or below 0.1 mCi in a week. Distances like 1.7 cm, 17 cm, or 0.17 m would produce far higher exposures than allowed.

The distance needed follows the inverse-square law: exposure rate from a point source is proportional to the activity divided by the square of the distance (rate ∝ A / r^2).

Convert the limit to the same units as the source:

0.1 mCi = 0.0001 Ci.

At 1 cm from a 3 Ci source, the rate is proportional to 3 Ci / (1 cm)^2. At distance r (in cm), the rate is 3 / r^2 Ci per unit time. Set this equal to the allowed weekly rate:

3 / r^2 = 0.0001

r^2 = 3 / 0.0001 = 30000, so r = sqrt(30000) ≈ 173 cm ≈ 1.73 m.

Therefore, about 1.7 meters are needed to keep exposure at or below 0.1 mCi in a week. Distances like 1.7 cm, 17 cm, or 0.17 m would produce far higher exposures than allowed.