Question

In an experiment reproducing the measurements of Rutherford and his co-workers, $22\times {10}^{-3}$ mg of He gas was collected in one year from a sample of radium. This sample was observed to emit $1.06\times {10}^{11}\alpha$ - particles per second. Thus, Avogadro's number is?

• A. $5.92\times {10}^{23}mo{l}^{-1}$
• B. $6.92\times {10}^{23}mo{l}^{-1}$
• C. $6.08\times {10}^{23}mo{l}^{-1}$
• D. $6.58\times {10}^{23}mo{l}^{-1}$

Answer 1

$22\times {10}^{-3}mgofHegaswascollectedinoneyearfromasampleofradium$

$22\times {10}^{-3}mgperyear=22\times {10}^{-6}gperyear$

$=\frac{22\times {10}^{-6}}{365\times 24\times 3600}gmpersecond$

$=6.976\times {10}^{-13}gmpersecond$

Thus, the mass of $1.06\times {10}^{11}\alpha -particles=6.976\times {10}^{-13}g$

Thus $4gmpermoleof\alpha particles=\frac{1.06\times {10}^{11}\times 4}{6.976\times {10}^{-13}}$

=$6.08\times {10}^{23}$

Conclusion- Hence, the correct option is C. Value of the Avogadro number is $6.08\times {10}^{23}$ .