Assuming an element's half-life is 3.6 years. How much of 2 grams of the element would remain after 10.8 years?
.25
k = 0.693/t1/2
Substitute into the below equation.
ln(No/N) = kt
No = 2 g from the problem.
N = to be calculated (how much is left)
k from above.
t = 10.8 years.
Solve for N
1.6
To determine how much of the element remains after a certain amount of time, we can use the formula for exponential decay: N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the time that has passed, and T is the half-life of the element.
In this case, the element has a half-life of 3.6 years, and we want to find out how much remains after 10.8 years. The initial amount is given as 2 grams.
Plugging in the values into the formula, we have:
N = 2 * (1/2)^(10.8/3.6)
To calculate this, we need to evaluate the exponent first, which is 10.8/3.6 = 3.
Now we can substitute this value into the equation:
N = 2 * (1/2)^3
Next, we calculate (1/2)^3, which is equal to 1/8.
Therefore, N = 2 * (1/8) = 1/4 grams.
After 10.8 years, 1/4 grams of the element would remain.