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Physics Half-Life

DECAY LAB V3
DECAY ACTIVE

HALF-LIFE CALCULATOR

RADIOACTIVE DECAY • N(t) = N₀e^(-λt)

REMAINING AMOUNT

316.2
ATOMS / UNITS
Fraction Remaining
31.62%
Number of Half-Lives
1.75
Exponential decay simulation active

RADIOACTIVE DECAY • HALF-LIFE MATRIX 2026

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Stability Hub

The Atomic Clock. Half-life is the Universal Ledger of Decay. It is the only metric that allows us to look back billions of years into a planet's history with mathematical certainty.

  • ⏳ Fixed Interval: The time required for a 50% state transition.
  • 📉 Exponential: Why radioactive material never truly hits "zero."
  • 🧱 Daughter Products: What's left behind after the decay is finished.
⏳
DECAY METRICS
PROBABILITY:
50% PER INTERVAL
STATUS: ✅ PREDICTABLE
DECAY-SYNC ACTIVE ✅

N-Naught Hub

The Origin Point. $N_0$ is the Atomic Heritage of a sample. It is the snapshot of matter at the very moment of creation, before the clock of decay begins to tick.

  • 🏁 t = 0: The absolute starting value of any decaying system.
  • 📈 Scaling Factor: The variable that determines the magnitude of the curve.
  • 🧱 Conservation: The sum of parents and daughters always equals N0.
🏁
INITIAL STATE DATA
VARIABLE (N0):
100.00%
STATUS: ✅ PRE-DECAY
START-SYNC ACTIVE ✅

Tempo Hub

The Rhythms of Decay. Half-life t₁/₂ is the Universal Constant of Change. It is the steady heartbeat of the atom, ticking away until matter transforms into its final, stable form.

  • ⏳ 0.693 / λ: The math that defines the survival of the nucleus.
  • 📉 Constant Rate: Why half-life never changes, regardless of sample size.
  • 🔬 Dating: The primary tool for unlocking the age of the solar system.
⏳
DECAY INTERVAL
VALUE t₁/₂:
50% REMAINING
STATUS: ✅ LOCKED CONSTANT
TEMPO-SYNC ACTIVE ✅

Time Hub

The Forward Arrow. Elapsed Time (t) is the Universal Progression. In the quantum realm, it is the variable that transforms potential energy into stable history.

  • ⏱️ t Variable: The actual duration recorded by the observer's clock.
  • 📉 Exponential Flow: How time dictates the depletion of the nucleus.
  • 🏹 Entropy: Why time only moves toward the decay of the parent atom.
⏱️
TEMPORAL METRICS
ELAPSED (t):
00:00:00:00
STATUS: ✅ RUNNING
TIME-SYNC ACTIVE ✅

Radioactive Decay

N = N0 e^(-λt)

N = Remaining quantity

N0 = Initial quantity

λ = Decay constant

t = Time elapsed