Correct Answer - Option 2 :
\(\frac{1}{8}\)
CONCEPT:
Radioactivity:
- Radioactivity is a process by which the nucleus of an unstable atom loses energy by emitting radiation.
- Two forces, namely the force of repulsion that is electrostatic and the powerful forces of attraction of the nucleus acts in the nucleus.
- These two forces are considered extremely strong in nature. The instability of the nucleus increases as the size of the nucleus increases because the mass of the nucleus becomes a lot to concentrate on.
- That’s the reason why atoms of Plutonium, Uranium are extremely unstable and show radioactivity.
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Half-life: Half-life is the time period after which half of the quantity of the radioactive element gets decayed.
CALCULATION:
Given Half-life = 2 years, total time = 6 years, and let the initial amount of radioactive substance (No) = 1
Since half-life is 2 years so 6 years is equal to 3 half-lives.
- We know that the fraction of substance remains after n half-lives,
\(\Rightarrow N'=\frac{N_{o}}{2^{n}}\)
Where N = amount remaining after n half-lives and No = initial amount
Let
\(\Rightarrow N'=\frac{N_{o}}{2^{3}}\)
\(\Rightarrow N'=\frac{N_{o}}{8}=\frac{1}{8}\)
- Hence, option 2 is correct.
