Decay factors for Concentration questions

Concentration Formula

$\frac{Activity}{Volume}$

$$\frac{Ci,Bq}{mL}$$

Decay Factor Concentration Formula

C_t = DF * C₀

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C₀ = Original concentration (eg concentration if prep’d at 8am)
C_t = Concentration at time of use (eg concentration when used at 12 pm)
DF = Decay Factor (decay within amount of time, eg 4 hours)

DF Concentration Formula EXAMPLE 1

150 mCi Tc 99m MDP is prepared at 8:00 AM, at a concentration of 15 mCi/mL. What is the concentration at 9:30 AM?

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C_t = ? mCi/mL 9:30 AM, C₀ = 15 mCi/mL 8:00 AM, DF = 0.941 for 1 hr 30 min

C_9:30 = 0.841 * 15 mCi/mL

C_9:30 = 12.62 mCi/mL

DF Concentration Formula EXAMPLE 2

A dose of I-123 MIBG was left out for an unknown amount of time. If the original concentration was 2 mCi/mL, but is now 1.5 mCi/mL, approximately how long was the dose left out?

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C₀ = 2 mCi/mL, C_t = 1.5 mCi/mL, DF = ? for ? h ? min

1.5 mCi/mL = DF * 2 mCi/mL
DF = 1.5/2 = 0.75

0.75 = DF at ~5 hours and 45 minutes, so that is about how long the dose had been left out

DF for Tc-99m at 30 min

DF 30 min = 0.994

DF for Tc-99m at 1 hour

DF 1 hour = 0.891

DF for Tc-99m at 1 hour, 30 min

DF 1 hour 30 min = 0.841

DF for Tc-99m at 2 hours

DF 2 hours = 0.794

DF for Tc-99m at 2 hours, 30 min

DF 2 hours 30 min = 0.750

DF for Tc-99m at 3 hours

DF 3 hours = 0.708

DF for Tc-99m at 3 hours, 30 min

DF 3 hours 30 min = 0.668

DF for Tc-99m at 4 hours

DF 4 hours = 0.631

DF for Tc-99m at 4 hours, 30 min

DF 4 hours 30 min = 0.596

DF for Tc-99m at 5 hours

DF 5 hours = 0.562

DF for Tc-99m at 5 hours, 30 min

DF 5 hours 30 min = 0.531

DF for Tc-99m at 6 hours

DF 6 hours = 0.501

DF for Tc-99m at 6 hours, 30 min

DF 6 hours 30 min = 0.473

DF for F-18 at 15 min

DF 15 min = 0.909

DF for F-18 at 30 min

DF 30 min = 0.826

DF for F-18 at 45 min

DF 45 min = 0.753

DF for F-18 at 1 hour (60 min)

DF 60 min = 0.683

DF for F-18 at 1 hour 30 min (90 min)

DF 90 min = 0.569

DF for F-18 at 1 hour 50 min (110 min)

DF 110 min = 0.500

DF for F-18 at 2 hours 30 min (150 min)

DF 150 min = 0.384

Fun fact! For any isotope halfway through one half-life, the decay factor will often be roughly 0.7!

Tc-99m at 3 hrs: DF =0.701

F-18 at 55 min: DF = 0.707

I-123 at 6.6 hrs: DF = 0.710

I-131 at 4 days: DF = 0.707