🌟 Big Idea: The rate at which radioactive substances decay is not random. There's a predictable pattern, and we can represent this with some cool equations!

• When you have a sample of radioactive material, not all nuclei decay instantly. Instead, they decay over time.
• We can look at the ratio:
  \(\frac {number\ of\ nuclei\ that\ decay\ soon}{inital\ number\ of\ nuclei}\)
  Surprise! This ratio is a constant for a specific radioactive substance (or nuclide).

Real-World Example: Imagine you have 100 ticking time bombs (eek! 😱). If 10 explode in the next minute, that's a 10% decay rate. If this ratio remains constant, then in the next minute, 10% of the remaining 90 bombs would explode.

• The "probability" an individual nucleus decays in a super short time interval is known as the decay constant, λ.
• So, Activity A (how fast things are decaying) can be found by multiplying the decay constant with the initial number of nuclei:
  A = λ × N

Did you know? Activity is the rate of change of N, and is given by
          A = − dtdN​ = λN
The negative sign? Oh, that’s just because as time goes on, there's less of the radioactive stuff left.