How much time in years (assume a 365 day yr) would it take for a 1.6678g sample of 239Np to decay to a mass of 0.8671g if it has a half life of 2.030*10^5s
metrtroll bessness collage
To calculate the amount of time it would take for a 1.6678g sample of 239Np to decay to a mass of 0.8671g, we need to determine the number of half-lives required for this decay process.
The half-life of a radioactive substance is the time it takes for half of the initial amount to decay. In this case, the half-life of 239Np is given as 2.030*10^5 seconds.
First, let's calculate the number of half-lives required to decay from 1.6678g to 0.8671g:
Initial mass = 1.6678g
Final mass = 0.8671g
Since each half-life reduces the mass by half, we can set up the following equation:
Final mass = Initial mass * (1/2)^(number of half-lives)
0.8671g = 1.6678g * (1/2)^(number of half-lives)
Next, let's isolate the variable 'number of half-lives':
(1/2)^(number of half-lives) = 0.8671g / 1.6678g
Now, take the logarithm of both sides of the equation to solve for the exponent:
log((1/2)^(number of half-lives)) = log(0.8671g / 1.6678g)
Using logarithmic properties, we can bring down the exponent:
(number of half-lives) * log(1/2) = log(0.8671g / 1.6678g)
Now, divide both sides by log(1/2) to solve for the number of half-lives:
number of half-lives = log(0.8671g / 1.6678g) / log(1/2)
Using a calculator, evaluate the right side of the equation:
number of half-lives ≈ 0.3778
Therefore, it would take approximately 0.3778 half-lives for the 1.6678g sample of 239Np to decay to a mass of 0.8671g.
Finally, multiply the number of half-lives by the half-life duration to calculate the total time required:
Total time = number of half-lives * half-life duration
In this case:
Total time ≈ 0.3778 * 2.030*10^5s
Evaluate the right side:
Total time ≈ 76684s
Since there are 365 days in a year and each day has 24 hours, we can calculate the total time in years:
Total time in years ≈ 76684s / (365 * 24 * 60 * 60s)
Evaluate the right side:
Total time in years ≈ 2.43 years
Therefore, it would take approximately 2.43 years for the 1.6678g sample of 239Np to decay to a mass of 0.8671g, assuming a half-life of 2.030*10^5 seconds.