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
k = 0.693/t1/2
Substitute k into the equation below.
ln(No/N) = kt
No = 1.6878
N = 0.8671
k fro above.
Solve for t (in seconds) and change to years.
Thank you so much DrBob222
To answer this question, we need to use the concept of radioactive decay and the formula for half-life.
The half-life of a radioactive substance is the time it takes for half of the initial sample 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 it would take for the sample to decay from 1.6678g to 0.8671g.
Initial mass = 1.6678g
Final mass = 0.8671g
To find the number of half-lives, we can use the formula:
Number of half-lives = ln(final mass / initial mass) / ln(0.5)
Number of half-lives = ln(0.8671g / 1.6678g) / ln(0.5)
Next, since the half-life is given in seconds, we need to convert the number of half-lives from seconds to years. We can do this by multiplying the number of half-lives by the length of each half-life in seconds.
Number of seconds in a year = 365 days * 24 hours * 60 minutes * 60 seconds = 31,536,000 seconds/year
Finally, we can calculate the time in years by dividing the total number of seconds by the number of seconds per year.
Time in years = (Number of half-lives) * (Half-life in seconds) / (Number of seconds in a year)
Now, let's plug in the given values and calculate the time in years:
Number of half-lives = ln(0.8671g / 1.6678g) / ln(0.5)
Number of seconds in a year = 31,536,000 seconds/year
Time in years = (Number of half-lives) * (2.030 * 10^5 seconds) / (31,536,000 seconds/year)
By following these steps and plugging in the given values, you can calculate the time in years it would take for the 1.6678g sample of 239Np to decay to a mass of 0.8671g.