1. What Is The Radioactive Decay Formula?

The radioactive decay formula describes how the quantity of a radioactive substance decreases over time. It follows an exponential decay pattern where the rate of decay is proportional to the current amount of the substance.

2. How Does The Calculator Work?

The calculator uses the radioactive decay formula:

Where:

• \( N \) — Remaining quantity after time t
• \( N_0 \) — Initial quantity at time t=0
• \( \lambda \) — Decay constant (probability of decay per unit time)
• \( t \) — Elapsed time
• \( e \) — Euler's number (approximately 2.71828)

Explanation: The formula shows that radioactive substances decay exponentially, with the decay rate characterized by the decay constant λ.

3. Importance Of Radioactive Decay Calculation

Details: Calculating radioactive decay is essential in nuclear physics, radiometric dating, medical imaging, radiation therapy, and nuclear safety. It helps determine the remaining radioactivity of a substance after a given period.

4. Using The Calculator

Tips: Enter the initial quantity (N₀), decay constant (λ), and time (t). All values must be positive numbers. The calculator will compute the remaining quantity (N) after the specified time.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between decay constant and half-life?
A: The half-life (T½) is related to the decay constant by the formula: T½ = ln(2)/λ ≈ 0.693/λ.

Q2: Can this formula be used for any radioactive element?
A: Yes, the exponential decay formula applies to all radioactive isotopes, though each has its own unique decay constant.

Q3: What units should I use for the decay constant?
A: The decay constant units must be consistent with the time units. For example, if time is in years, λ should be in per year.

Q4: How accurate is this decay model?
A: The exponential decay model is highly accurate for large numbers of atoms and is the standard model used in nuclear physics.

Q5: What if I know the half-life instead of the decay constant?
A: You can calculate the decay constant from the half-life using λ = ln(2)/T½.