Radium-221 has a half life of 30 sec. How long will it take for 85% of a sample to decay?

Question

I have tried to figure this question out and still cant get it right.

Answer 1

 

Hi Kristen,

 

With a half life time of 30s,

the equation for the remaining Radium-221 can be written as

 

     R(t) = R₀·(1/2)^t/30         (Eq. 1)

 

where R₀ is the initial amount and t is the elapsed time in seconds.

 

With 85% decayed, Eq. 1 is written as

 

     0.15R₀ = R₀·(1/2)^t/30

 

     0.15 = (1/2)^t/30

 

     2^t/30 = 1/0.15

 

     (t/30) = log₂(1/0.15)

              

     t = 30·log2(1/0.15)

 

       = 82.109

 

The answer is 82.109 sec.