Decay Curve

Contents

Key Stage 5

Meaning

A decay curve is an exponential decrease curve showing how the mass or activity of a radioactive isotope decreases with time.

About Decay Curve

• The decay curve represents the rate of decay of a radioactive substance.
• The decay curve shows the characteristic exponential decay pattern of radioactive materials.
• The decay curve is used to determine the half-life of a radioactive substance.
• The decay curve helps in understanding the stability and longevity of isotopes.

Formula

The curve is described by the equation

\(𝑁(𝑡)=𝑁_0𝑒^{−𝜆𝑡}\)

\(𝑁(𝑡)=𝑁_02^{−𝑡/𝑡_{1/2}}\)

Where:

𝑁(𝑡) is the number of undecayed nuclei at time (𝑡)

𝑁₀ is the initial number of nuclei

𝑡 is the time reading from the start of the experiment

𝜆 is the decay constant for the isotope.

t_1/2 is the half-life of a given isotope

Examples

• The decay curve of Uranium-238 showing its decrease over millions of years.
• Monitoring the decay curve of medical isotopes to ensure they remain effective for treatment.