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
Nam D. · LM
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#

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