A particular radioactive element has a half life of 10.0 days. How much is left after 30.0 days if the sample started with 345g?
3 half-lives
345 * 1/2 * 1/2 * 1/2
To determine how much of the radioactive element is left after a certain amount of time, we can use the equation:
Final amount = Initial amount * (1/2)^(t/h)
where:
- Final amount is the amount of the element remaining after time t
- Initial amount is the initial amount of the element
- t is the amount of time that has passed
- h is the half-life of the element
In this case, the initial amount is 345g, the half-life is 10.0 days, and the time is 30.0 days. Plugging these values into the equation, we have:
Final amount = 345g * (1/2)^(30.0 days / 10.0 days)
Simplifying this equation gives:
Final amount = 345g * (1/2)^3
Final amount = 345g * (1/8)
Final amount = 43.125g
Therefore, after 30.0 days, there will be approximately 43.125g of the radioactive element remaining.
To determine how much of the radioactive element is left after 30.0 days, we can use the formula for radioactive decay:
N(t) = N₀ * (½)^(t / t₁/₂)
Where:
- N(t) is the amount of the radioactive element remaining after time t.
- N₀ is the initial amount of the radioactive element.
- t₁/₂ is the half-life of the radioactive element.
In this case, the initial amount N₀ is 345g, the time t is 30.0 days, and the half-life t₁/₂ is 10.0 days.
Substituting these values into the formula:
N(30.0) = 345g * (½)^(30.0 days / 10.0 days)
Simplifying the equation:
N(30.0) = 345g * (½)^3
Now, let's calculate the value of (½)^3:
(½)^3 = 1/2 * 1/2 * 1/2 = 1/8
Substituting this value back into the equation:
N(30.0) = 345g * 1/8
Now, let's multiply the values:
N(30.0) = 345g * 1/8
= 43.125g
Therefore, after 30.0 days, there will be approximately 43.125g of the radioactive element left.