Radium decomposes at a rate proportional to the amount present. If half the orignal amount disappears in 1600 yrs, then the percentage loss in 100 years is ( . Given . 2=0.6912 & e ^ -0 04320 =0 9576 )

Step-by-step solution

Let R= Amount of radium present at time t . We have d R d t R d R t =k R d R k = kdt R=kt+C ...(1) when t=0 , let R=R₀ so we get R₀=0+c c= R R R₀ =kt( ) When t=1600 yrs , R = 1 2 R₀ 1 2 R₀ R₀ =1000 1 2 -1000 k k= 1 1000 1 2 - 1 1000 (0-k g₂ )= -00012 1000 k=-0.000432t When t =100 , we get R R₀ =-0.0432 R R₀ =e⁻⁴⁰⁴³ R R₀ =0.9576 R=0.9576 R₀ % loss = R₀-0.9576 R₀ R₀ 100 %=0.0424 100 %=4.24 %