After two hours, 1/16 of the initial amount of a radioactive isotope remains undecayed. What is the half-life of the isotope?
one half =1/2 left
two half=1/4
three half=1/8
four half=1/15
one halflive=1/4 * 2hours=30 min
To determine the half-life of a radioactive isotope, we need to use the information given in the question. Let's break it down step by step.
1. Start with the information given: After two hours, 1/16 of the initial amount remains undecayed. This means that 15/16 (1 - 1/16) of the isotope decayed in those two hours.
2. Now, we need to find out how long it takes for half of the initial amount to decay. Knowing that 1/16 decayed after two hours, we can multiply that fraction by 2 (to obtain 1/8) to find out how long it would take for half of the isotope to decay.
3. If 1/8 of the isotope decays in a specific time period, we can multiply that time period by 2 to find the half-life. In this case, since 1/8 decays in two hours, the half-life of the isotope would be 4 hours (2 x 2 = 4).
Therefore, the half-life of the isotope is 4 hours.