Correct Answer - Option 2 : 1620 year

**Concept:**

**Decay constant:**

The time required for half of the original population of radioactive atoms to decay is called the half-life.

The relationship between the half-life, T_{1/2}, and the decay constant is given by,

\(T_{1/2}=\frac{0.693}{λ}\)

**Calculation:**

Given,

λ = 1.3566 × 10-11 s-1

From the above concept,

\(T_{1/2}=\frac{0.693}{λ}=\frac{0.693}{1.3566\times 10^{-11}}=5.1083\times10^{10}\ sec\)

Conversing second into the year,

\(5.1083\times10^{10}\ sec=\frac{5.1083\times10^{10}}{365\times24\times3600}=1620\ year\)