Question

The half-life of radon is 3.8 days. Three fourth of a radon sample decay in
A. 5.02 days
B. 15.2 days
C. 7.6 days
D. 11.4 days

Answer 1

Hint: In this question, we need to find the days taken to decay three fourths of a radon sample. By using the radioactive decay formula, we will find the days.

Formula Used
The amount of substance that will decay is given by
\[\dfrac{N}{{{N_0}}}\]= \[{(\dfrac{1}{2})^n}\]
Here, \[{N_0}\] is the amount of substance that will initially decay and \[N\] is the quantity that still remains.
\[t = n \times {T_{1/2}}\]
Here, \[{T_{1/2}}\] is half-life, and n is the number of half-life.

Complete step by step solution:
Half-life is the amount of time required for half of the radioactive atoms in a sample to disintegrate into a more solid form. I Radon is an inert gas that as a result does not readily endure chemical reactions: it can dissolve in water but does not combine with other atoms to form molecules.

Given,
Half-life of radon \[{T_{1/2}}\] = 3.8 days
We know that, Decayed fraction = \[\dfrac{3}{4}\],
so undecayed fraction = \[\dfrac{1}{4}\].
We know that the amount of substance that will decay is
\[\dfrac{N}{{{N_0}}}\]= \[{(\dfrac{1}{2})^n}\]
\[\Rightarrow \dfrac{1}{4}\]= \[{(\dfrac{1}{2})^n}\]
Therefore, Number of half-life n = 2

To find the days taken to decay three fourth of a radon sample, we can use
\[t = n \times {T_{1/2}}\]
By substituting n=2, we get
$t = 2 \times 3.8 = 7.6\,days$
Therefore, t = 7.6 days ie Three fourth of a radon sample decay in 7.6 days.

Therefore the correct answer is Option C.

Additional Information: Radon is an odorless, colorless gas, a radioactive by-product of radium. It is part of the natural radioactive decay series that begins with uranium-238. It is radioactive with a half-life of 3.8 days, decaying by the emission of alpha particles to polonium, bismuth, and lead in sequential steps. Radon is present outdoors and is usually found at very low levels in surface water (like lakes and rivers) and in outdoor air. It is available at higher levels in the air in houses and other buildings, and also in water from underground sources, like private well water.

Radon is a radionuclide, meaning that, as time passes, suffers radioactive decay. Every radionuclide has a half-life, which is the time required for half of the radioactive particles present to decay away. In a country like France, radon is liable for 34% of the total radiation exposure felt by the population. These levels differ considerably from one location to another, with uranium-rich granite soil that releases more radon than sedimentary rocks.

Note: To solve this question, it is necessary to remember the formula and define the radon’s half-life. In the decay chain, students can see that radon has a half-life of 3.8 days. If they make mistakes here, then the result will be wrong. So, it is necessary to do the calculations carefully.