The half-life of Th-232 is 1.4E10. Find the number of disintegrations per hour emitted by 1 mol of Th-232.
1.4E10 what unit? days, hours, seconds?
k = 0.693/t1/2 = approx 4.95E-11
Rate at time zero = k*N and for 1 mol Th, N will be 6.02E23 atoms.
Solve for R, which will be in disintegrations/year . Convert that to d/hour.
years
The assumption for my response was years.
To find the number of disintegrations per hour emitted by 1 mol of Th-232, we can use the formula for radioactive decay:
N(t) = N(0) * (1/2)^(t/T)
Where:
N(t) = number of remaining atoms at time t
N(0) = initial number of atoms
t = time
T = half-life of the substance
Given that the half-life of Th-232 is 1.4E10 (14 billion) years, we need to convert it to hours because we want the disintegrations per hour. There are 365.25 days in a year and 24 hours in a day, so the conversion factor is:
Conversion factor = (365.25 days/year) * (24 hours/day)
Now, we substitute the values into the formula:
N(t) = 1 mol * (1/2)^(t/T)
N(0) is 1 mol because we are considering 1 mol of Th-232.
We can rearrange the formula to solve for N(t):
N(t) = 1 mol * (1/2)^(t/T)
N(t) = 1 mol * (1/2)^(t / (1.4E10 hours))
Now, we need to determine the value of t. We want to find the number of disintegrations per hour, so t will be 1 hour.
N(1 hour) = 1 mol * (1/2)^(1 / (1.4E10 hours))
Now, we can substitute the values into the equation and calculate the number of disintegrations per hour of 1 mol of Th-232.