indium-115 has a half life of 4.5 hours, if you start with a 12.0mg sample of indium-115, how much will remain after 13.5 hours
two ways: remaining=12mg*(1/2)^13.5/4.5
you can do that by putting this in your google search window:12*(1/2)^(13.5/4.5)=
Nerd way:
remaining=12.5*e^(.693*13.5/4.5)=
and put that in your google search window
k = 0.693/t1/2
Solve for k and substitute into the below equation.
ln(No/N) = kt
No = 12.0 mg
N = ? mg
k = from above
t = 13.5 hrs
To determine how much indium-115 will remain after 13.5 hours, we can use the concept of radioactive decay and the half-life of indium-115. Here's how you can calculate it:
1. Start by finding out the number of half-lives that have passed. Since the half-life of indium-115 is 4.5 hours, divide the total elapsed time (13.5 hours) by the half-life:
Number of half-lives = total elapsed time / half-life
= 13.5 hours / 4.5 hours
= 3 half-lives
2. Now, use the number of half-lives to calculate the remaining amount of indium-115. Each half-life reduces the amount of indium-115 by half. So, raise 0.5 to the power of the number of half-lives:
Remaining amount = initial amount × (1/2)^(number of half-lives)
= 12.0mg × (1/2)^3
= 12.0mg × (1/8)
= 1.5mg
Therefore, after 13.5 hours, there will be 1.5mg of indium-115 remaining from the initial 12.0mg sample.