An $\alpha$-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 $1.12\times {10}^{-2}mL$at STP.  The number of $\alpha$ particles emitted

4gm of Helium volume is 22400 ml at STP

Now, $1.12\times {10}^{-2}ml$ of  He, at STP weighs  $\frac{4\times 1.12\times {10}^{-2}}{22400}$

$=2\times {10}^{-6}$ gms of He

4 gms of He contains $6\times {10}^{23}$ atoms of He

$2\times {10}^{-6}gm$ of He contains  $\frac{2\times {10}^{-6}\times 6\times {10}^{23}}{4}$$=3\times {10}^{17}atoms$

Since no. of $\alpha$  particles emitted is equal to no. of  He atoms produced

No. of $\alpha$ particles `$=3\times {10}^{17}$