Assuming a half-life of 1599 years, how many years will be needed for the decay of 16/15 of a given amount of radium-226?

1 Answer
Apr 10, 2018

6396 years

Explanation:

I'm assuming that you meant 15/16 of the substance has decayed, instead of 16/15, as that just sounds absurd.

Using the half-life equation,

A=[A_0]e^(-lambdat)

  • [A_0] is the initial amount of substance

  • lambda is the decay constant, lambda=(ln2)/t_(1/2), where t_(1/2) is the half-life of the substance

  • t is the time in years

According to your question, 15/16 has been decayed, so only 1/16 remains, and therefore:

A=1/16[A_0]

1/16[A_0]=[A_0]e^(-lambdat)

e^(-lambdat)=1/16

-lambdat=ln(1/16)

lambdat=-ln(1/16)

t=(-ln(1/16))/(lambda)

=-ln(1/16)*(t_(1/2))/ln2

=-ln(1/16)*1599/ln2

=6396