The half-life of a radioactive isotope represents the average time it would take

Question

The half-life of a radioactive isotope represents the average time it would take half of a collection of this type of nucleus to decay. For example, you start with a sample of 1000 Oxygen-15 (15O) nuclei, which has a half-life of 122 seconds. After 122 seconds, half of the 15O nuclei will have decayed into Nitrogen-15 (15N) nuclei. After another 122s, half of the remaining Oxygen nuclei will have also decayed, and so on.

A) Suppose you start with 4040 15O nuclei and zero 15N nuclei. How many 15O nuclei remain after 122 s has passed?

B) How many 15N nuclei are there after 122 s has passed?

C) How many 15O nuclei remain after 244 s has passed?


D) How many 15N nuclei are there after 244 s has passed?

E) Suppose you start with 3460 Carbon-14(14C) nuclei. 14C has a half-life of 5730 years and decays into Nitrogen-14(14N) via a beta decay. How much time has passed if you are left with 1730 14C nuclei? (The units for years is 'yr'.)

F) How much time has passed if you are left with 865 14C nuclei?

Explanation / Answer

A. 4040 / 2 = 2020

B. 2020 (see above)

C. 1010

D. 2020 + 1010 = 3030

E. 5730 years (one full decay happened)

F. 5730 * 2 = 11460

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