If 250mg of a radioactive element decays to 200mg in 48 hours, find the half-life of the element.
ln(No/N) = kt
No=250 mg
N = 200 mg
t = 48 hours.
Solve for k, then put k into the following equation and solve for t1/2.
k = 0.693/t1/2
To find the half-life of the radioactive element, we can use the equation:
ln(No/N) = kt
Where:
No represents the initial amount of the element (250mg),
N represents the final amount of the element (200mg),
k is the decay constant,
and t is the time period (48 hours).
First, let's solve for k:
ln(No/N) = kt
ln(250/200) = k * 48
ln(1.25) = k * 48
k = ln(1.25) / 48
Next, let's substitute the decay constant k into the half-life equation:
k = 0.693 / t1/2
0.693 / t1/2 = ln(1.25) / 48
Now, we can solve for t1/2 by rearranging the equation:
t1/2 = (0.693 * 48) / ln(1.25)
t1/2 ≈ 104.7 hours
Therefore, the half-life of the radioactive element is approximately 104.7 hours.