Question

(a) What are radioactive isotopes? Give two examples of radioactive isotopes.
(b) Give any two uses of radioactive isotopes.
(c) An element Z contains two naturally occurring isotopes ${}_{17}{}^{35}\mathrm{Z}$ and ${}_{17}{}^{37}\mathrm{Z}$. If the average atomic mass of this element be 35.5 u, calculate the percentage of two isotopes.

Answer 1

(a) Radioactive isotopes are those isotopes of an element which have an unstable nucleus. Because of this, the radioactive isotopes undergo radioactive decay by emitting alpha, beta, and gamma radiation to gain the stability of the nucleus. For eg, O¹⁵, Co⁶⁰, etc.

(b) Uses of radioactive isotopes:
(i) Radioactive isotopes are used to determine the age of rocks and minerals.
(ii) It is used to treat cancer, detect blood clots and diagnose thyroid.

(c) Let the percentage of ${}_{17}{}^{35}\mathrm{Z}$ = X
Then the percentage of ${}_{17}{}^{37}\mathrm{Z}$ = 100 $-$ X
Average atomic weight of Z = 35.5u
Now,
$$\begin{gathered} 35.5=\frac{35.\mathrm{X}+37.(100-\mathrm{X})}{100} \\ \Rightarrow 35.5=\frac{35\mathrm{X}+3700-37\mathrm{X}}{100} \\ \Rightarrow 35.5\times 100=3700-2\mathrm{X} \\ \Rightarrow 3550-3700=-2\mathrm{X} \\ \Rightarrow -150=-2\mathrm{X} \\ \Rightarrow \mathrm{X}=75 \end{gathered}$$

Therefore, ${}_{17}{}^{35}\mathrm{Z}$ = 75% and, ${}_{17}{}^{37}\mathrm{Z}$ = 100$-$75 = 25%