Question

Uranium disintegrates at a rate proportional to the amount present at any time. If M1 and M2 grams of uranium are present at T1 and T2 respectively, show that the half-life of uranium is: ( ( (T2-T1) ln2 ) / (ln (M1/M2) ) ).

Answer 1

Like this?
\[\frac{(T2-T1) \times \ln2}{\ln (\frac{M1}{M2})}\]

Answer 2

yes @anhhuyalex

Answer 3

HINT: we write the rrate of disintegration equation as dM1/M1 = kdT1 and like wise for M2, solving, we get an ODE which we integrate to obtain the amount of uranium present at time T1. This is given as M1 = M10 exp(-kT1) and M2 = M20 exp(-kT2). so it seems the rates are same for both masses. Note that M10 and M20 are initial masses of uranium present at T1=T2 + 0. Then we simplify considering same rate of disintegration to get ur equation. Nw, continue the simplification to get ur solution.

Answer 4

T1=T2 = 0 is d initial time for masses M10 and M20