A vial of 67Ga-citrate calibrated at 0600 PST contains how much activity at 1200 EST the next day?

To determine how much activity remains in a vial of 67Ga-citrate calibrated at 0600 PST when measured at 1200 EST the following day, one must first convert the time zone correctly and then calculate the decay based on the half-life of the isotope.

The half-life of Gallium-67 is approximately 78.3 hours. First, it is essential to establish the total time elapsed between the calibration datetime and the measurement datetime.

0600 PST is equivalent to 0900 EST (since PST is 3 hours behind EST). If you calculate the period from 0900 EST the day of calibration to 1200 EST the following day, it totals 27 hours.

With the elapsed time established, you can use the radioactive decay formula to calculate the remaining activity. The formula for decay is:

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

Where:

• ( A ) is the final activity,

• ( A_0 ) is the initial activity,

• ( t ) is the elapsed time,

• ( T_{1/2} ) is the half-life.

Assuming the vial was calibrated at 6.0