It is found from an experiment that the radioactive substance emits one beta particle for each decay process. Also an average of 8.4 beta particles are emitted each second by 2.5 milligram of substance. The atomic weight of substance is 230. What is the half-life?

Solution

The activity = 8.4 sec^-1.
Atomic weight of the substance = 230 kg

Number of atoms in kilomole (i.e., 230 kg) = 6.02 x 10²⁶Therefore,
^{Number of atoms,    $N = \frac{6.02 \times 10^{26}}{230} \times 2.5 \times 10^{- 6}$

$= 6.54 \times 10^{18}$

$\Rightarrow$ $8.4 = λN = λ \times 6.54 \times 10^{18} λ = \frac{8.4 \times 10^{- 18}}{6.54} = 1.28 \times 10^{- 18} / \sec$}Half-life, $T = \frac{0.693}{λ}$

   $= \frac{0.693}{1.28 \times 10^{- 18}} = 5.41 \times 10^{17} \sec$

   $= \frac{5.41 \times 10^{17}}{3.16 \times 10^{7}} = 1.7 \times 10^{10} years .$

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Wave Optics

It is found from an experiment that the radioactive substance emits one beta particle for each decay process. Also an average of 8.4 beta particles are emitted each second by 2.5 milligram of substance. The atomic weight of substance is 230. What is the half-life?

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