Calcium 47 is used for scanning bones. If 53 grams of a 250 gram calcium 47 sample is left after 30 hours what is the half life?

Question

Find out by using N=N0(1/2)^t/h

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use to solve half-life questions is

N = N0 * (1/2)^(t/h)

In this case we know that

N = final amount = 53 grams

N0 = initial amount = 250 grams

t = time elapsed = 30 hours

h = half life = what we are trying to solve for

plugging those values in yields

53 = 250 * (1/2)^(30/h)

From there then you want to solve for the value of “h” using logarithms! When I do that I end up getting h = 13.41, meaning that the half-life of Calcium-47 is about 13.41 hours.

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The given formula is N=N₀*(1/2)^(t/h) => 53 =250*0.5^(30/h) => 0.212 = 0.5^(30/h) => Log 0.212 = (30/h)*log 0.5 Then h= (30*log (0.5))/(log 0.212) = 30*0.30103/0.67366 = 13.40 hrs