42-7 Measuring Radiation Dosage

42-7 Measuring Radiation Dosage#

Prompts

  • Define absorbed dose. What is the SI unit (gray)? Why is it energy per unit mass, not total energy?

  • What is equivalent dose and how does it differ from absorbed dose? What role does RBE (relative biological effectiveness) play?

  • Alpha particles cause more biological damage per unit absorbed energy than gamma rays. Why? How does RBE reflect this?

  • A person receives 0.1 Gy from gamma rays and 0.01 Gy from alpha particles. Which exposure is more hazardous? Calculate the equivalent doses (use RBE ≈ 1 for gamma, ≈ 20 for alpha).

  • Activity (Bq) measures decays per second. How does activity relate to dose? Why can’t we infer dose from activity alone?

Lecture Notes#

Overview#

  • Absorbed dose measures the energy deposited by ionizing radiation per unit mass of tissue. The SI unit is the gray (Gy) = 1 J/kg.

  • Equivalent dose accounts for the fact that different types of radiation cause different biological damage for the same absorbed energy. It is absorbed dose × RBE (relative biological effectiveness), measured in sieverts (Sv).

  • Activity (section 42-3) measures the decay rate (Bq); it does not directly give dose — the dose depends on the type of radiation, distance, shielding, and exposure time.

Absorbed Dose#

The absorbed dose \(D\) is the energy deposited by ionizing radiation per unit mass of the absorbing material:

(459)#\[ D = \frac{E_{\text{dep}}}{m} \]

SI unit: the gray (Gy): \(1\ \text{Gy} = 1\ \text{J/kg}\).

The older unit, the rad (radiation absorbed dose), is \(1\ \text{rad} = 0.01\ \text{Gy} = 10^{-2}\ \text{J/kg}\).

Why per unit mass?

Different tissues and organs have different masses. Dose per unit mass allows comparison across body parts and individuals. It also reflects the local energy density that drives ionization and damage.

Equivalent Dose and RBE#

The biological effect of radiation depends not only on how much energy is deposited but also on how it is deposited. Dense ionization (e.g., alpha particles) causes more damage per unit energy than sparse ionization (e.g., gamma rays).

The relative biological effectiveness (RBE) is the ratio of doses needed to produce the same biological effect: if radiation type \(X\) requires dose \(D_X\) and a reference (e.g., gamma) requires \(D_{\text{ref}}\), then \(\text{RBE}_X = D_{\text{ref}}/D_X\). Higher RBE means more damage per unit absorbed dose.

The equivalent dose \(H\) is

(460)#\[ H = D \times \text{RBE} \]

SI unit: the sievert (Sv). For gamma rays and electrons, RBE ≈ 1, so \(H \approx D\) in Sv.

Radiation

Typical RBE

Gamma rays, X-rays, \(\beta\)

~1

Protons, fast neutrons

~5–20

Alpha particles

~20

Why alpha is more damaging

Alpha particles are heavy and charged; they ionize densely along a short track. Gamma rays spread energy over a larger volume. For the same absorbed dose (J/kg), alpha creates more clustered damage to DNA and cells.

Activity vs. Dose#

Activity \(R\) (section 42-3) is the number of decays per second (Bq). It characterizes the source, not the effect on a person.

Dose depends on:

  • Activity of the source

  • Type of radiation (alpha, beta, gamma)

  • Distance from the source (inverse-square for point sources)

  • Shielding (absorption in material)

  • Exposure time

  • Geometry (internal vs. external, organ targeted)

A high-activity gamma source far away may give a lower dose than a low-activity alpha source ingested (alpha is stopped by skin but damages internal tissue if inside the body).

Summary#

  • Absorbed dose: \(D = E_{\text{dep}}/m\); unit gray (Gy) = 1 J/kg.

  • Equivalent dose: \(H = D \times \text{RBE}\); unit sievert (Sv); accounts for biological damage.

  • RBE: alpha ~20, gamma/\(\beta\) ~1; denser ionization → higher RBE.

  • Activity (Bq) measures source strength; dose depends on activity, radiation type, distance, shielding, and time.