Question

The mass of $radon-222$ corresponding to $1$ $Curie$ will be, (its half is 3.8 days)

• A. $6.46\times {10}^{-8}$ $gm$
• B. $64.60\times {10}^{-7}$ $gm$
• C. $6.46\times {10}^{-10}$ $gm$
• D. $64.60\times {10}^{-10}$ $gm$

Answer 1

The correct option is B $64.60\times {10}^{-7}$ $gm$

Activity is $1Curie=3.7\times {10}^{10}decayspersecond$

Half-life is $3.8\times 86400=328320seconds$

Number of active atoms left is $3.7\times {10}^{10}\times 328320/0.693=17.53\times {10}^{15}atoms$

The mass of these atoms is $3.686\times {10}^{-22}\times 17.53\times {10}^{15}gm=64.60\times {10}^{-7}gm$