1. What is Exponential Decay?

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. This model is commonly used in chemistry to describe radioactive decay, drug metabolism, and chemical reactions.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

Where:

• Initial amount — Starting quantity of substance (grams or moles)
• k — Decay constant (1/time units)
• t — Elapsed time (same time units as k)
• e — Base of natural logarithm (~2.71828)

Explanation: The formula calculates how much of a substance remains after time t, given its initial amount and decay rate.

3. Importance of Residual Value Calculation

Details: Calculating residual values is crucial for determining drug dosages, radioactive material safety, chemical reaction kinetics, and understanding biological processes.

4. Using the Calculator

Tips: Enter the initial amount in grams or moles, decay constant in reciprocal time units (e.g., 1/sec, 1/hour), and time in matching units. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: How is the decay constant (k) determined?
A: The decay constant is typically determined experimentally or can be calculated from half-life (k = ln(2)/half-life).

Q2: What's the relationship between half-life and decay constant?
A: Half-life (t½) = ln(2)/k. The decay constant is inversely proportional to half-life.

Q3: Can this be used for radioactive decay?
A: Yes, radioactive decay follows first-order kinetics and can be modeled with this equation.

Q4: What units should I use?
A: Ensure time units match between k and t. Common units are seconds, minutes, hours, or days.

Q5: How accurate is this model?
A: It's exact for first-order decay processes. For complex systems, additional factors may need consideration.