Question

The half-life period of $_{53}{{I}^{125}}$ is 60 days. What % of radioactivity would be present after 240 days?

Answer 1

Hint: It is given that half life of radioactive isotope of iodine is 60 days. So, in 60 days the concentration of iodine is reduced to half its original concentration. Iodine undergoes 4 half life in 240 days. The % of radioactivity after 240 days can be calculated by the below formula:
$%\text{ left = }\frac{\frac{{{[\text{A }\!\!]\!\!\text{ }}_{0}}}{{{2}^{n}}}}{{{[\text{A }\!\!]\!\!\text{ }}_{0}}}\text{ x 100 }$
Where,
${{[\text{A }\!\!]\!\!\text{ }}_{0}}$ is the initial concentration of the radioactive element,
n is the number of half lives spent by the radioactive element.

Complete answer:
Radioactive decay also known as radioactive disintegration or nuclear disintegration is the process by which an unstable atomic nucleus loses energy in the form of radiation to gain stability. Any material containing unstable nuclei is considered radioactive.
Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emission of either protons or photons as to release energy.
- Alpha decay involves the release of an alpha particle from the nucleus.
- Beta decay is said to occur when the atom either releases an electron and an antineutrino of a positron and a neutrino.
- In gamma decay, a radioactive nucleus first decays by the emission of either an alpha or a beta particle. The resultant product is still in an excited state and it decays to a lower energy state by emitting a gamma ray or photon.
We know that the total number of half-lives spent is 4.
Substituting the values in the formula,
$%\text{ left = }\frac{\frac{{{[\text{A }\!\!]\!\!\text{ }}_{0}}}{{{2}^{n}}}}{{{[\text{A }\!\!]\!\!\text{ }}_{0}}}\text{ x 100 }$
$%\text{ left = }\frac{1}{{{2}^{4}}}\text{ x 100 }$
$%\text{ left = 6}\text{.75 }$
The % of radioactivity present after days is 6.75%.

The correct answer is option (C).

Note: Radioactive decay as a controlled reaction is used for production of electricity by disintegrating uranium atoms. However nuclear reactions can become uncontrolled if proper care is not taken in reducing the decay rate. Uncontrolled nuclear reactions emit radiation that can cause havoc to mankind as the radiation affects the proper functioning of the human body.