How To Calculate Beta Decay

Beta Decay Equation:

\[ A = A_0 e^{-\lambda t} \]

Activity After Beta Decay (A):

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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. The exponential decay law describes how the activity of a radioactive substance decreases over time.

2. How Does The Calculator Work?

The calculator uses the beta decay equation:

\[ A = A_0 e^{-\lambda t} \]

Where:

\( A \) — Activity after time t (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 exponential decay where the activity decreases exponentially with time, with the decay constant determining the rate of decay.

3. Importance Of Beta Decay Calculation

Details: Calculating beta decay activity is crucial for nuclear medicine, radiation safety, radioactive dating, and understanding nuclear processes in various scientific and medical applications.

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 valid (positive values for activity and decay constant, non-negative time).

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: \( T_{1/2} = \frac{\ln(2)}{\lambda} \).

Q2: What are typical units for radioactive activity?
A: Activity is measured in becquerels (Bq) in SI units, where 1 Bq = 1 decay per second. The curie (Ci) is also commonly used (1 Ci = 3.7×10¹⁰ Bq).

Q3: How accurate is the exponential decay model?
A: The exponential decay model is highly accurate for large numbers of atoms and is fundamental to radioactive decay physics.

Q4: Can this calculator be used for other types of radioactive decay?
A: Yes, the exponential decay law applies to all types of radioactive decay, including alpha and gamma decay.

Q5: What factors can affect beta decay rates?
A: Beta decay rates are generally constant and unaffected by external conditions like temperature and pressure, unlike chemical reaction rates.