half-life question?

Question

Different isotopes are useful in different dating processes. Suppose we wished to determine the age of an object which we suspect to be approximately 100 years old. An isotope with which of the following half-lives would be most appropriate for this project?

5 years
50 years
500 years
5,000 years

Answer 1

500 years

Answer 2

I know very little about this but I would say the 50 years half-life would work best. The 5 year one would reduce the amount of the isotope to (1/2)^20 of it's original amount and I would guess that this would make it difficult to determine how much of the original is present assuming less than perfect instrumentation. 500 and 5000 years would leave too little of the isotope having decayed and lead to inaccuracies in measuring this amount. 50 years and there would be 1/4 of the original isotope left and 3/4 having decayed. This ratio of 3 to 1 seems like it would give the highest probability of the most accurate measurements.

Answer 3

500 years and 5,000 years are too large. 50 years would probably be good. 5 years may be too small, but I am not totally sure.

Say Plutonium has a half life of 1000 years. Then, every 1000 years in storage, it's radioativity cuts in half. Today, it is 100%. In the year 3,000, it's at 50%. In the year 4,000, it's 25%. In the year 5,000, it's 12.5%.

So say something has a half life of 5 years, then by the time it is 100 years old, it has been diluted so much that it may not be very detectable.

0 years - 100%
5 years - 50%
10 years - 25%
15 yrs - 12.5%
20 yrs - 6.25%
25 yrs - 3.125%
30 yrs - 1.5.....%
35 yrs - 0.75....%
40 yrs - very low
getting lower
& lower

So you see, something with a half life of five years would not be a very good isotope to use.

Answer 4

100 / 2 = 50

Answer 5

50 years

Answer 6

hmmmm. . . . 50 yrs? idk