How do you calculate the amount of a radioactive substance remaining after an integral number of half-lifes have passed?
No/N = 2^n
No number initially.
N = number remaining.
n = number of half lives.
To calculate the amount of a radioactive substance remaining after an integral number of half-lives have passed, you can use the radioactive decay formula:
N(t) = N₀ * (1/2)^(t / t₁/₂)
Where:
- N(t) is the remaining amount of the substance at time t
- N₀ is the initial amount of the substance
- t is the total time that has passed
- t₁/₂ is the half-life of the substance
To calculate the remaining amount, follow these steps:
1. Determine the initial amount of the substance (N₀).
2. Determine the half-life of the substance (t₁/₂).
3. Determine how many half-lives have passed (t / t₁/₂).
4. Substitute the values into the formula: N(t) = N₀ * (1/2)^(t / t₁/₂).
5. Calculate N(t) to find the remaining amount of the radioactive substance.
Note: Make sure to use consistent units for time (e.g., seconds, minutes, hours) and the same units for the initial amount and the remaining amount.
To calculate the amount of a radioactive substance remaining after an integral number of half-lives have passed, you can use the following formula:
Amount remaining = Initial amount * (1/2)^(number of half-lives)
Here's how you can use this formula step-by-step:
1. Determine the initial amount of the radioactive substance. This could be given in units such as grams or becquerels.
2. Identify the number of half-lives that have passed. If you're given a specific time, you can divide it by the half-life of the substance to determine the number of half-lives. If you're given the number of half-lives directly, you can skip this step.
3. Plug the values into the formula. Multiply the initial amount by the fraction (1/2) raised to the power of the number of half-lives.
4. Calculate the result. This will give you the remaining amount of the radioactive substance after the specified number of half-lives.
Remember to use the same units consistently throughout the calculation.
Keep in mind that this formula assumes that the decay of the radioactive substance follows a first-order exponential decay model.