Radioactive Decay Law and Activity

Radioactive Decay Law and Activity

What is it?

The radioactive decay law describes the exponential decrease in the number of undecayed radioactive nuclei with time. Activity is the rate at which radioactive nuclei decay.

In simple words

• Both number of nuclei and activity decrease exponentially.

Full school-level explanation

The radioactive decay law describes the exponential decrease in the number of undecayed radioactive nuclei with time. Activity is the rate at which radioactive nuclei decay.

Activity

If `N` nuclei remain: dN/dt = −λN where `λ` is the decay constant. Solving gives: N=N₀e⁽-λt) where: `N₀` = initial number of radioactive nuclei. Activity `R` or `A_r` is: R = −dN/dt Therefore: R=λN Initial activity: R₀=λN₀ Thus: R=R₀e⁽-λt)

SI Unit

Activity is measured in: becquerel (Bq) 1 Bq = 1 decay per second

Formula / Key Relation

**dN/dt=−λN** **N=N₀e⁽−λt)** **R=λN**

Remember

• R = −dN/dt
• R=λN
• R₀=λN₀
• R=R₀e⁽-λt)
• becquerel (Bq)
• 1 Bq = 1 decay per second
• dN/dt=−λN
• N=N₀e⁽−λt)

Deeper understanding

Go deeper on Radioactive Decay Law and Activity: connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Decay

Exam focus

Quick revision

• R = −dN/dt
• R=λN
• R₀=λN₀
• R=R₀e⁽-λt)
• Activity: If `N` nuclei remain: dN/dt = −λN where `λ` is the decay constant. Solving gives: **N=N₀e^(-
• SI Unit: Activity is measured in: becquerel (Bq) 1 Bq = 1 decay per second

For long answers on Radioactive Decay Law and Activity: define clearly → explain the main parts → give one example → state one exam caution.