Question

The curie was originally intended to be the activity of one gram of radium-226, $[T_{50}=1620a$,here 'a' stands for annum (year) in SI unit$]$. Calculate actual weight of radium which is equivalent to one curie.
given $1a=3.1536\times {10}^{7}s$
Plan $-\frac{dN}{dt}=-\lambda N=-\lambda \frac{w}{A}{N}_0$
Thus, w (mass of the radioactive substance) can be calculated.

• A. $1.024$ g
• B. $2.024$ g
• C. $1.424$ g
• D. None of these

Answer 1

The correct option is A $1.024$ g

$\lambda =\frac{0.693}{1620}=\frac{0.693}{1620\times 3.1536\times {10}^7}{s}^{-1}$
but by definition,1 Ci(curie)$=3.7\times {10}^{10}$ dps
$-\frac{dN}{dt}=\lambda N$
$3.7\times {10}^{10}=\frac{0.693}{1620\times 3.1536\times {10}^7}$ N
$N=2.72766\times {10}^{21}$ atoms
moles of Ra-226$=\frac{2.72766\times {10}^{21}}{6.02\times {10}^{23}}$
$=0.004531$
amount in g $=mol\times 226$
$=1.024$ g