Physics – 5.2.3 Radioactive decay | e-Consult

(a)

At time t=0, the activity (A) is given by:

A₀ = (N/2)⁰ = N

Where N is the initial number of radioactive atoms.

We are given a 500g sample. To calculate N, we need the molar mass of the isotope. Let's assume the isotope is Carbon-14 (¹⁴C) with a molar mass of 14g/mol.

N = 500g / 14g/mol = 35.71 mol

Number of atoms = N * Avogadro's number = 35.71 mol * 6.022 x 10²³ atoms/mol = 2.15 x 10²⁵ atoms.

Therefore, A₀ = 2.15 x 10²⁵ Bq.

At time t=20 years, the activity is:

A(20) = (N/2)^20/10 = (N/2)² = (N/4)

A(20) = (2.15 x 10²⁵ Bq) / 4 = 5.38 x 10²⁴ Bq.

(b)

The half-life of a radioactive isotope is the time it takes for half of the radioactive nuclei in a sample to decay. It is a useful property because it allows us to:

• Determine the age of ancient objects (radiocarbon dating).
• Monitor the rate of decay of radioactive materials.
• Predict the amount of a radioactive substance remaining after a certain time.

The half-life is constant for a given radioactive isotope and is independent of temperature, pressure, and chemical conditions. This makes it a reliable indicator of the age of a sample.