Question

Tc-99m is a common radioisotope used in medical imaging. It is a metastable isotope that emits low energy gamma radiation (140 keV) with a half-life of roughly 6 hours. This half-life is extremely long for a metastable state, which makes it useful for studying gamma emission. This particular radioisotope has a biological half-life of roughly 1 day while in a human, and an atomic mass of 1.627 × 10−25 kg/atom.

1. What is the effective half-life of Tc-99m while in a patient? h
2. If a patient is injected with 1.41 nanograms of Tc-99m, what is the initial activity of the Tc-99m immediately after being injected into the patient?         Bq
3. What will be the activity due to the Tc-99m left in the patient’s body after 9.5 hours?             Bq

Answer 1

Part a)

Te=effective half-life

Tp=physical half-life = 24 hour

Tb=biological half-life = 6 hour

Te = (Tp * Tb )/ (Tp + Tb )

Placing values ,

Te = ( 24 * 6 ) (24 + 6 )

= 4.8 hour

Part b )

R= (0.693*N') / Te(half life ) .... (1)

R = activity

N'= no of atoms = 1.41 * 10-12kg / 1.627 × 10-25 kg/atom

=8.66 * 1012 atoms

Placing values in the equation

R = (0.693 * 8.66 * 1012)/ 4.8

= 1.25 * 1012 decays hr-1 or 3.37*108 decays per second(Bq)

Part c)

First we will calculate the amount left , then we will apply the equation (1)

.....( 2

N0 = initial quantity = 1.41 * 10 -12kg

N = quantity at time t

t = 9.5 hour

λ =decay constant = ln (2) / Te ( half life )

λ *t = (ln (2) *t )/ Te ( half life )

Placing values we get

λ = 1.372

Placing values in eq 2

N = 1.41 * 10 -12kg ( e -1.372)

= 3.576 * 10 -13kg

So the no of atoms (N' ) = 3.576 * 10 -13kg /1.627 × 10-25 kg/atom

= 2.198 * 1012 atoms

Placing values in eq 1)

R = (0.693*N') / Te(half life)

= 3.173 * 1011 decays per hour or 8.815 * 107 decays per second (Bq)