Question

TWO DIFFERENT RADIOACTIVE ELEMENTS WITH HALF LIVES T1 AND T2 HAVE N1 AND N2(UNDECAYED) ATOMS RESPECTIVELY PRESENT AT A GIVEN INSTANT.DETERMINE THE RATIO OF THEIR ACTIVITIES AT THIS INSTANT

Answer 1

Number of atoms (undecayed yet) at time t are N1 and N2.
Activity or, the rates of decaying at this moment (time = t), are = R1 and R2.
λ1 and λ2 are the decay constants of the materials.
$T1_{1/2}\ and\ T2_{1/2}$ are the half life periods of the radio active materials.

$N1 = N1_0*e^{-\lambda_1 t}\\\\R1=Activity=decay\ rate=-\frac{dN1}{dt}=\lambda_1 N1_0*e^{-\lambda_1 t}\\\\\lambda_1=\frac{Ln\ 2}{T_{1/2}}\\\\R1=\frac{Ln 2 *N1}{T1_{1/2}}}\\\\\frac{R1}{R2}=\frac{N1\ T2}{N2\ T1}$