Help! I suck at half-life questions!?

An earlier answer has the mass, but I think activity would measure the rate of decay events. Given:

m(t) = m(0) * 2^(-t/h) .... h = half life

dm/dt = m(0) * (-log 2 / h) * 2^(-t/h) = -m(t) * (log 2) / h

That's the number of kg disappearing per second (using SI). A Ga-68 atom has mass 67.928 amu = 1.1280 x 10^-25 kg. So, activity measured in decays/sec is:

A(t) = | dm/dt | * 1/(1.1279709e-25 kg/decay)

A(t) = m(t) * [(log2)/h * (8.8655 x 10^24 decays/kg)]

That constant factor in [] brackets converts current mass in kg of Ga-68 to activity in decays/s (bequerels or Bq.)

Basically every 68 minutes you have half as much as the prior period.

The formula is:

A(t) = Ao * ½^(t/λ)

Ao : initial amount (0.23 mg)

t : time (same units as half-life)

λ : half-life (68 minutes)

In this case, you have been given the time as 3 hours, so we just need to convert that to 180 minutes and plug it in.

A(t) = 0.23 * ½^(180/68)

A(t) ≈ 0.0367 mg