1. What is Beta Decay?

Beta decay is a type of radioactive decay in which a beta particle (electron or positron) is emitted from an atomic nucleus. This process transforms a neutron into a proton or vice versa, changing the element while conserving mass number.

2. How Does the Calculator Work?

The calculator uses the beta decay equation:

Where:

• \( A \) — Activity after decay (Bq)
• \( A_0 \) — Initial activity (Bq)
• \( \lambda \) — Decay constant (s⁻¹)
• \( t \) — Time elapsed (s)
• \( e \) — Euler's number (approximately 2.71828)

Explanation: The equation describes the exponential decrease in radioactive activity over time, following the fundamental law of radioactive decay.

3. Importance of Beta Decay Calculation

Details: Accurate beta decay calculations are essential for nuclear medicine, radiation safety, radiometric dating, nuclear power applications, and understanding fundamental particle physics.

4. Using the Calculator

Tips: Enter initial activity in becquerels (Bq), decay constant in inverse seconds (s⁻¹), and time in seconds. All values must be positive (time can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between decay constant and half-life?
A: The decay constant (λ) and half-life (T½) are related by: λ = ln(2)/T½, where T½ is the time for activity to reduce by half.

Q2: What are typical decay constant values?
A: Decay constants vary widely depending on the isotope. For example, Carbon-14 has λ ≈ 3.8394×10⁻¹² s⁻¹, while Iodine-131 has λ ≈ 9.975×10⁻⁷ s⁻¹.

Q3: Can this calculator be used for other decay types?
A: Yes, the exponential decay equation applies to all types of radioactive decay (alpha, beta, gamma), though the decay constant values differ.

Q4: What is the difference between Bq and Ci?
A: Becquerel (Bq) is the SI unit (1 decay per second), while Curie (Ci) is the traditional unit (3.7×10¹⁰ Bq). This calculator uses Bq for consistency with SI units.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for the exponential decay model. Accuracy depends on the precision of input values and the assumption of constant decay probability.