Question

The half-life of ${}^{226}$Ra is 1602 year. The activity of 0.1g of RaCl${}_2$ assuming all the Ra atoms are ${}^{226}$Ra and mass of Cl atom 35.5g/mol is

• A. $1.8\times {10}^8$ dps
• B. $2.8\times {10}^8$ dps
• C. $1.8\times {10}^9$ dps
• D. $2.8\times {10}^9$ dps

Answer 1

Answer: (D)

$2.8\times {10}^9$ dps

The number of Ra atom present, $N=\frac{0.1}{226+2\left(35.5\right)}\times 6.023\times {10}^{23}=20.28\times {10}^{19}$

Decay constant $\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{1602\times 3.154\times {10}^7}=1.37\times {10}^{-11}{s}^{-1}$ where $1year=3.154\times {10}^{7}s$

Activity $=N\lambda =20.28\times {10}^{-19}\times 1.37\times {10}^{-11}\sim 2.8\times {10}^9$ dps (decay per second)