# If it is known that the decay constant of radium is 1.3566 × 10-11 s-1 then find its half-life. (Given atomic mass of radium is 226.095 amu)

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If it is known that the decay constant of radium is 1.3566 ×  10-11 s-1 then find its half-life. (Given atomic mass of radium is 226.095 amu)
1. 1000 year
2. 1620 year
3. 1785 year
4. 1467 year

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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, T1/2, 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,

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