Radioactive Decay and Inverse Square Law - Flashcards

A set of practice flashcards covering decay formulas, half-life, decay constant, inverse square law, and dose concepts with worked examples.

What does the decay formula describe about activity over time?

The activity at time t, At, decreases according to At = A0 e^{-0.693 (t/t{1/2})} (also written At = A0 e^{-λ t}).

What is the inverse square law in radiation dose?

Radiation dose rate is inversely proportional to the square of the distance from the source: I ∝ 1/d^2.

What is a half-life?

The time required for half of the original radioisotope to decay; a constant characteristic of the nuclide.

What is the decay constant (λ) and its alias?

The fraction of atoms decaying per unit time; also called the disintegration constant.

How are half-life and decay constant related?

λ = 0.693 / t{1/2} and t{1/2} = 0.693 / λ.

What does A_t represent?

Activity at time t.

What does A_0 represent?

Initial activity at time t = 0.

What is the decay factor (DF)?

DF = e^{-0.693 (t/t{1/2})}; used in At = A0 × DF and DF is always < 1.

How do you solve for A0 when At and t are known (At = A0 e^{-0.693 t/t_{1/2}})?

A0 = At × e^{0.693 t/t_{1/2}}.

Example: If A0 = 200 mCi, t = 3 h, t{1/2} = 6 h, what is A_t?

Approximately 141.4 mCi.

Example: Ga-67 with A0 = 30 mCi at 8:00 Monday, t = 48 h, t{1/2} = 78 h. What is A_t at 8:00 Wednesday?

Approximately 19.6 mCi.

What is the pre-calibration factor (PCF)?

A factor used to relate At to A0 in kit preparation; A0 = At × PCF; PCF is typically > 1.

What is the purpose of the pre-calibration factor in radiopharmaceutical kits?

To adjust the activity to the desired starting activity for kit preparation; compensates for calibration differences.

What are absorbed dose, equivalent dose, and effective dose?

Absorbed dose measures energy deposited per mass; Equivalent dose accounts for radiation type; Effective dose estimates lifetime risk across tissues.

Under NRC rules, when is dosimetry required?

When a worker is likely to receive about 10% of the annual dose limits (limits provided for eyes, skin, extremities, whole body, and internal organs).

What does the layman’s form of the inverse square law say?

If distance doubles, exposure becomes one-quarter; I1 D1^2 = I2 D2^2.

If exposure is 20 mrem/h at 1 ft, what is it at 2 ft?

5 mrem/h.

If exposure is 20 mrem/h at 1 ft, what is it at 3 ft?

Approximately 2.2 mrem/h.

If a source produces 350 mrem/h at 3 inches, what is the exposure rate at 36 inches?

Approximately 2.4 mrem/h.

What is the equation used to determine the initial activity Ao needed to achieve a desired At in the future?

Ao = At e^{0.693 t/t{1/2}} (rearranged from At = Ao e^{-0.693 t/t{1/2}}).

What is a daughter product in radioactive decay?

The decay product produced when a radionuclide decays (the product of decay).