The half-life of $_{38}^{90} Sr$ is $28$ years. What is the disintegration rate of $15 \; mg$ of this isotope?

$A$ source contains two phosphorus radionuclides $_{15}^{32} P \left(T_{1/2} = 14.3 \ d\right)$ and $_{15}^{33} P \left(T_{1/2} = 25.3 \ d\right)$. Initially,$10\%$ of the decays come from $_{15}^{33} P$. How long must one wait until $90\%$ of the decays come from $_{15}^{33} P$?

The decay constant for a radioactive nuclide is $1.5 \times 10^{-5} \, s^{-1}$. The molar mass of the substance is $60 \, g \, mol^{-1}$,$(N_A = 6 \times 10^{23})$. The activity of $1.0 \, \mu g$ of the substance is $....... \times 10^{10} \, Bq$.

$A$ $280\, \text{day}$ old radioactive substance shows an activity of $6000\, \text{dps}$. $140\, \text{days}$ later, its activity becomes $3000\, \text{dps}$. What was its initial activity? ......... $\text{dps}$

$A$ small quantity of solution containing $Na^{24}$ radionuclide of activity $1 \, \mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1 \, cm^3$ taken after $5 \, hours$ shows an activity of $298$ disintegrations per minute. What will be the total volume of the blood in the body of the person? Assume that the radioactive solution mixes uniformly in the blood of the person. (Take $1 \, Ci = 3.7 \times 10^{10}$ disintegrations per second and $e^{-\lambda t} = 0.7927$; where $\lambda$ is the disintegration constant and $t = 5 \, hours$.)

The half-life of radium is $1600 \, \text{years}$. After how many years will $25 \, \text{g}$ of radium remain from $100 \, \text{g}$ of radium?