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An α - particle changes into a Helium atom. In the course of one year the volume of Helium collected from a sample of Radium was found to be 1.12×10^–2mL at STP. The number of α - particles emitted by the sample of Radium in the same time is

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6 × 10¹⁷

3 × 10¹⁷

1.5 × 10¹⁷

1.2 × 10¹⁸

answer is B.

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Detailed Solution

Ra - isotope α-emission He gas

We know that α-particles are double positively charged Helium nuclei.α-rays change to Helium gas.

Volume of He gas = 1.12 $\times$ 10^-2 ml at STP

22400cc of the He at STP contain 6.023 $\times$ 10²³He-atoms

1.12 $\times$ 10^-2cc of He at STP contain 'X' atoms

\large X = \frac{1.12 \times 10^{-2}\times6.023\times10^{23}}{22400} = 3 \times 10^{17}

Number of α-particles emitted = 3 $\times$ 10¹⁷

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