Radioactive Decay Calculation: Activity of one milli Curie of P-Labelled ATP After 60 Days

Calculate the activity of one milli Curie of P-labelled ATP after 60 days. If the half life is 12 days.
(a) 125 micro Curie
(b) 250 micro Curie
(c) 62.5 micro Curie
(d) 31.25 micro Curie

Final Answer: (D) 31.25 µCi

Thus, the correct answer is (D) 31.25 µCi. This aligns with the principles of radioactive decay, where each half-life reduces the substance’s activity by half.

Understanding Radioactive Decay

Radioactive decay is a natural process in which an unstable isotope loses energy by emitting radiation. The rate of decay is measured by a parameter known as the half-life, which is the time required for half of the radioactive substance to decay. The decay follows an exponential pattern, meaning that after each half-life, only 50% of the remaining substance remains.

In this problem, we have P-labeled ATP with:

• Initial Activity = 1 milliCurie (mCi) = 1000 microCurie (µCi)
• Half-life = 12 days
• Total time elapsed = 60 days

Understanding the Concept

Radioactive isotopes decay over time based on their half-life. A half-life is the time required for half of a radioactive substance to decay. In this case, the half-life of P-labeled ATP is 12 days, so the activity decreases as follows:

• After 12 days → 1000 → 500 µCi
• After 24 days → 500 → 250 µCi
• After 36 days → 250 → 125 µCi
• After 48 days → 125 → 62.5 µCi
• After 60 days → 62.5 → 31.25 µCi