Isotope Decay & Specific Activity Calculator

This tool helps you calculate the remaining activity of a radioactive isotope after a certain period and determine its specific activity.

Select Isotope

Initial Activity ($A_o$)

Elapsed Time ($t$)

Results

Remaining Activity ($A_t$): 0 Bq

Decay Constant ($\lambda$): 0 s⁻¹

Specific Activity ($SA$): 0 Bq/g

Underlying Principles

Radioactive decay is a process where an unstable atomic nucleus loses energy by emitting radiation. This process is characterized by a half-life ($T_{1/2}$), the time required for the activity of a substance to fall to half of its initial value.

The core decay formula is:

$$A_t = A_o e^{-\lambda t}$$

The decay constant $\lambda$ and half-life $T_{1/2}$ are related by:

$$ \lambda = \frac{0.693}{T_{1/2}} $$

Specific Activity (SA) is the activity per unit mass, which can be calculated using the decay constant, Avogadro's number ($N_A$), and the atomic mass ($A_w$):

$$SA = \frac{\lambda N_A}{A_w}$$