1 g of radium is known to emit 3.7 × 1 0 10 particles per second. The half-life period of radium (Atomic weight of radium = 226 ) is (in years)

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TestHub · Accepted Answer

Number of radium atoms in 1 g of radium = $\frac{6.02 \times 1 0 ^{23}}{226} = 2.66 \times 1 0^{21}$

$- \frac{d N}{d t} = λ N$

So, $λ = - \frac{- \frac{d N}{d t}}{N} = \frac{3.7 \times 1 0 ^{10}}{2.66 \times 1 0 ^{21}} = 1.39 \times 1 0^{- 11} s^{- 1}$

Half-life, $t_{1/2} = \frac{0.693}{λ} = \frac{0.693}{1.39 \times 1 0 ^{- 11}} = 5 \times 1 0^{10} s$

$5 \times 1 0^{10} s = \frac{5 \times 1 0 ^{10}}{60 \times 60 \times 24 \times 365} = 1585 ye a rs .$

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