Question

Which statement about radioactive equilibrium is incorrect?
A. it is also called secular equilibrium
B. the equilibrium is attained when parent atom has ${{t}_{{}^{1}/{}_{2}}}$more than ${{t}_{{}^{1}/{}_{2}}}$ of daughter element.
C. the equilibrium is attained when $\lambda$of parent element is more than daughter element.
D. no equilibrium if ${{t}_{{}^{1}/{}_{2}}}$ of parent element is less than ${{t}_{{}^{1}/{}_{2}}}$ of daughter element.

Answer 1

Radioactivity is the phenomena which involves the reaction between the nuclei of the elements. Such types of elements are termed as radioactive elements. ${{t}_{{}^{1}/{}_{2}}}$ is the half life of any radioactive nucleus, $\lambda$is the decay constant. Radioactive equilibrium happens when the reacting species and the products formed decay at the same rate.

Complete answer:
Radioactive equilibrium is the phenomena where the reacting radionuclide and the radionuclide formed from its reaction, both decay at the same rate as to their proportions remain constant. There are various conditions in which radioactive equilibrium is achieved.
The correct statements about the radioactive equilibrium are:
-Radioactive equilibrium is known as secular equilibrium when the parent nucleus has a very long half life than the daughter nucleus.
- radioactive equilibrium does not happen when half life of parent nucleus is less than half life of daughter nucleus, which means that parent atom should have ${{t}_{{}^{1}/{}_{2}}}$ more than${{t}_{{}^{1}/{}_{2}}}$ of daughter atom. This happens as the activity of the reactants rises initially, which then becomes the same as that of the products being formed, so a slightly greater half life of the parent atom is necessary for the radioactive equilibrium.
This shows that option C is incorrect.
As the decay constant is inverse to the mean life of any radioactive nucleus, if the decay constant, $\lambda$ is more for a parent atom, this means it has a less life, and thus a less half life. When $\lambda$for a parent nucleus is greater than that of daughter nucleus than the half life of the parent nucleus will be less, thus no equilibrium is attained.
Hence, the equilibrium is attained when $\lambda$of parent element is more than daughter element is the incorrect option.

Note:
Parent nucleus is the nucleus which is reacting to decay, while daughter nucleus is the product forming from the decay. When the difference between the half lives of the parent nucleus is slightly larger from the daughter nucleus, it is called transient radioactive equilibrium. And secular when the parent nucleus has a very huge half life than daughter nucleus.