3.2 ALARA and Protection Calculations

ALARA—As Low As Reasonably Achievable—is the central operational philosophy of radiation safety. Regulatory dose limits are upper bounds, not targets. A technologist who routinely approaches the annual limit without justification is failing ALARA even if still “legal.” NRC licensees must have an ALARA program; CNMT questions test both the definition and the three classic controls: Time, Distance, and Shielding.

Time

Dose is proportional to exposure time for a constant dose rate:

Dose ≈ dose rate × time

Cut the time in half → cut the dose in half (same geometry and source strength).

NMT applications:

• Plan before you touch activity. Read the prescription, prepare paperwork, open the shield path, and set the syringe shield before uncapping the vial.
• Minimize hold time of a loaded syringe. Draw, assay, label, and inject efficiently; do not chat while holding 25 mCi of Tc-99m at waist height without a shield.
• Practice non-radioactive technique (mock draws, venipuncture setup) so live draws are smooth.
• Therapy doses (I-131 capsules/liquid, Lu-177) deserve extra pre-planning—high activity means every extra second at close range matters.

Time control fails when technologists improvise at the bench with an unshielded source “just for a second.” Seconds add up across a career.

Distance and the Inverse Square Law

For an approximate point source in free space (valid enough for many exam problems and for sources small compared with distance):

[ I_1 d_1^2 = I_2 d_2^2 ]

or

[ \frac{I_2}{I_1} = \left(\frac{d_1}{d_2}\right)^2 ]

Intensity (or dose rate) falls with the square of distance.

Worked example 1 — Doubling distance

A vial measures 40 mR/h at 20 cm. What is the approximate rate at 40 cm?

[ I_2 = 40 \times \left(\frac{20}{40}\right)^2 = 40 \times \left(\frac{1}{2}\right)^2 = 40 \times 0.25 = \mathbf{10\ mR/h} ]

Doubling distance → one-fourth the intensity.

Worked example 2 — Find a safer distance

A source reads 90 mR/h at 30 cm. How far must you stand for 10 mR/h?

[ 10 \times d_2^2 = 90 \times 30^2 ] [ d_2^2 = \frac{90 \times 900}{10} = 8100 \quad \Rightarrow \quad d_2 = 90\ \text{cm} ]

Moving from 30 cm to 90 cm (3× distance) drops rate by 9× (90 → 10).

Worked example 3 — Quick mental math

Tripling distance → 1/9 intensity. Halving distance → 4× intensity (dangerous when leaning over a generator column).

NMT distance habits:

• Stand back during elution; do not hover over the elution shield.
• Use tongs/forceps for unshielded or lightly shielded sources when practical.
• Place high-activity waste and storage pigs away from the work station and seating areas.
• Remember inverse square is less perfect for large area sources, scatter, and room geometry—but exam math almost always assumes point-source inverse square.

Shielding: HVL, TVL, and Materials

Shielding inserts attenuating material between source and person. Photon attenuation is approximately exponential:

[ I = I_0 e^{-\mu x} ]

Half-value layer (HVL): thickness that reduces intensity to ½. Tenth-value layer (TVL): thickness that reduces intensity to 1/10.

Rough relationships (exam-friendly):

• 1 TVL ≈ 3.3 HVL (because (2^{3.3} ≈ 10))
• After n HVLs: intensity ≈ (I_0 / 2^n)
• After n TVLs: intensity ≈ (I_0 / 10^n)

Example

If HVL for a given photon energy in lead is 0.3 mm, then 0.9 mm (~3 HVL) reduces intensity to about 1/8 of the unshielded value.

Material selection in nuclear medicine

Syringe shields (tungsten or leaded glass window designs) dramatically cut extremity and body dose during draw and injection. Vial shields keep multi-dose kits and generators safer. Never remove a shield “to see better” unless policy and dose justify a momentary unshielded step—and even then, maximize distance and minimize time.

Beta caveat (high-yield)

Betas stop in low-Z plastic with less bremsstrahlung. Putting a pure beta source in a thin lead cup without enough low-Z absorber can increase penetrating x-ray hazard. Acrylic first, lead as secondary if required for any secondary photons.

Practical NMT ALARA Applications

1. Generator elution: Use the elution shield; stand back; assay with tongs/carrier; store in a pig promptly.
2. Kit preparation: Keep bulk Tc-99m shielded; use a syringe shield when reconstituting; never leave multi-dose vials unshielded on the counter.
3. Injection: Draw behind shield, assay, transport in a carrier, inject with the syringe shield on when technique allows.
4. PET (511 keV): Thicker shields; never cradle a loaded PET syringe against the body.
5. Therapy / waste: Maximize time-distance-shielding and contamination control; keep decay-in-storage away from desks; survey before release.

Exam traps: unshielded fingertip holds during difficult IVs; hovering over an elution; high-activity pigs at chest height; treating the 5 rem/year limit as a target instead of a ceiling.

On stacked problems, solve in order: time → inverse square → HVL/TVL. Keep survey units (mR/h) separate from activity (mCi/MBq). ALARA is arithmetic with your feet, clock, and pigs—not abstract ethics.