Question

During Nuclear explosion, one of the products is $$^{90}Sr$$with half –life of 28.1 years. If 1 µg of $$^{90}Sr$$was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if not lost metabolically?

Answer 1

Hint: Nuclear explosion is an explosion that occurs due to the release of the energy from a high speed nuclear reaction. The nuclear reactions are of two types, they are nuclear fission and fusion.
Half-life is the time at which the concentration of the reactant is exactly half of the initial concentration of the reactant molecules.

Complete step by step answer:
Nuclear fission is when the electrons or the nuclei break into two smaller nuclei. Additional neutrons are also released that can initiate a chain reaction. When each atom splits, a tremendous amount of energy is released. The most commonly used elements for the nuclear fission process are uranium and plutonium.
Nuclear fusion is when the two or more electrons bond together to form the bigger atom, for example: two hydrogen atoms fuse to form one helium atom. Nuclear fusion reactions are those reactions in which two lighter nuclei fuses together to form the bigger nuclei and thus the heat energy is absorbed in the process.
Given: Half –life =28.1 year.
We know that: $$K = \dfrac{{0.693}}{{{t_{1/2}}}} = \dfrac{{0.692}}{{28.1}}$$
Thus for the first order reaction:$t = \dfrac{{2.303}}{k}\log \dfrac{a}{{(a - x)}}$
$ a = 1\mu ,t = 60year,k = \dfrac{{0.693}}{{28.1}}year $
$ \Rightarrow 60year = \dfrac{{2.303}}{{\dfrac{{0.693}}{{28.1}}}} \times \log \dfrac{a}{{(a - x)}} $
$\Rightarrow \log \dfrac{a}{{(a - x)}} = \dfrac{{(60year) \times (\dfrac{{0.693}}{{28.1}})}}{{2.303}} $
$\Rightarrow 0.642 $
$\Rightarrow \dfrac{a}{{(a - x)}} = anti\log 0.642$
$\Rightarrow 4.385 $
$\Rightarrow (a - x) = \dfrac{a}{{4.385}} = 0.2280\mu g $

Thus the amount left will be 0.2280µg.
Uses of Nuclear Fission:
They are used in the thermoelectric generators for the space mission.
They are used in the nuclear power plants.
They are used for the treatment of cancer such as in the radiotherapy.

Note: No combustion reaction occurs in the nuclear fusion reaction and thus it is the environmentally friendly process posing less threat to the environment and thus in the process a lot of heat energy is consumed.