If a vial of 99mTc contains 4.65MBq at 0800, what is its concentration at 0930?

To calculate the concentration of 99mTc in the vial at 0930, we first need to understand the decay of the radionuclide over time. The half-life of technetium-99m (99mTc) is approximately 6 hours, or 360 minutes.

Starting with the activity at 0800, which is 4.65 MBq, we can determine how much of that activity remains after 1.5 hours (or 90 minutes) by using the decay formula:

[ A_t = A_0 \times (0.5)^{(t/T_{1/2})} ]

Where:

• ( A_t ) is the activity at time ( t )

• ( A_0 ) is the initial activity (4.65 MBq)

• ( t ) is elapsed time in minutes (90 minutes in this case)

• ( T_{1/2} ) is the half-life (360 minutes for 99mTc)

First, we calculate the fraction of the half-life that corresponds to 90 minutes:

[ \frac{90}{360} = 0.25 ]

Now we apply this fraction in the decay formula:

[ A_{