Enter the initial amount, decay constant, and time into the calculator to determine the remaining amount of a substance based on the Bateman equation. This calculator helps in understanding the decay process of radioactive substances or any process that follows first-order kinetics.
Bateman Equation Formula
The Bateman equation is used to calculate the remaining amount of a substance after a certain period of time, given its initial amount and decay constant. The formula is:
N = N0 * e^{(-λ * t)}Variables:
- N is the remaining amount of the substance
- N0 is the initial amount of the substance
- λ (lambda) is the decay constant, which is the probability per unit time that a particle will decay
- t is the time elapsed
To calculate the remaining amount, multiply the initial amount by the exponential of the negative product of the decay constant and time.
What is the Bateman Equation?
The Bateman equation is a fundamental equation in nuclear physics and chemistry that describes the behavior of radioactive decay chains. It is also applicable to any process that can be described by first-order kinetics, such as certain chemical reactions or biological processes. The equation provides a way to predict the quantity of a substance that remains after a period of time, assuming that the decay process is the only significant factor affecting the quantity.
How to Calculate Using the Bateman Equation?
The following steps outline how to calculate the remaining amount using the Bateman Equation.
- First, determine the initial amount of the substance (N0).
- Next, determine the decay constant (λ).
- Then, determine the time elapsed (t).
- Use the Bateman equation: N = N0 * e^(-λ * t).
- Finally, calculate the remaining amount (N).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Initial amount of the substance (N0) = 100 units
Decay constant (λ) = 0.1 per minute
Time elapsed (t) = 5 minutes
