1. What is the Decay Factor?

The decay factor (DF) represents the fraction of a quantity that remains after exponential decay over time. It is calculated using the formula \( DF = e^{-kt} \), where k is the decay rate constant and t is time.

2. How Does the Calculator Work?

The calculator uses the exponential decay formula:

Where:

• \( k \) — Decay rate constant (per unit time)
• \( t \) — Time elapsed (time units)
• \( e \) — Euler's number (approximately 2.71828)

Explanation: The formula calculates the remaining fraction of a substance undergoing exponential decay, which is common in radioactive decay, chemical reactions, and biological processes.

3. Importance of Decay Factor Calculation

Details: Calculating decay factor is essential in various scientific fields including nuclear physics, pharmacology, chemistry, and environmental science for predicting remaining quantities of decaying substances over time.

4. Using the Calculator

Tips: Enter the decay rate constant (k) and time (t) in consistent units. Both values must be positive numbers (k > 0, t ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What does the decay factor represent?
A: The decay factor represents the fraction of the original quantity that remains after time t, ranging from 0 (complete decay) to 1 (no decay).

Q2: How is decay factor related to half-life?
A: Half-life (\( t_{1/2} \)) is related to the decay constant by \( t_{1/2} = \frac{\ln(2)}{k} \). At half-life, DF = 0.5.

Q3: What are typical units for k and t?
A: Units must be consistent (e.g., if k is in per second, t must be in seconds). Common units include per second, per minute, per hour, or per year.

Q4: Can decay factor be greater than 1?
A: No, decay factor always ranges from 0 to 1. A value of 1 means no decay has occurred, while 0 means complete decay.

Q5: What are some practical applications?
A: Radioactive dating, drug metabolism studies, chemical reaction kinetics, population decline modeling, and material degradation analysis.