Question

1 g of radium produces 0.043 $c{m}^3$ of helim gas at STP in one year. The number of $\alpha$-particles produced in the same period is $11.6\times {10}^{17}$. Calculate the value of Avogadro's number.
Plan One mole $=22400c{m}^3$ at $STP=N_0$
Thus, from the volume of the gas and number of particles, $N_0$ can be determined.

• A. $6.043\times {10}^{23}mo{l}^{-1}$
• B. $8.063\times {10}^{23}mo{l}^{-1}$
• C. $7.043\times {10}^{23}mo{l}^{-1}$
• D. None of these

Answer 1

The correct option is A $6.043\times {10}^{23}mo{l}^{-1}$

${}_{88}Ra{⟶}_{86}Rn{+}_2^{4}He$
thus, 0.043 $c{m}^3$ of helium gas at STP
$=11.6\times {10}^{17}\alpha$-particles
$\therefore 22400c{m}^3$ of helium at STP$=\frac{11.6\times {10}^{17}}{0.043}\times 22400$
$N_0=6.043\times {10}^{23}mo{l}^{-1}$