Question

The activity of a certain sample of radioactive element '$A$' decreases to $1/\sqrt{2}$ of its value in $4$ days. What is its half life? Assuming that,
${}_Z^{M}A{-}_2^{4}He⟶$ ${}_{Z-2}^{M-4}B$
what mass of the sample will be left over after $24$ days if we start with one gram of '$A$'? Calculate this in terms of $M$.

Answer 1

Case I $A=\frac{A_0}{\sqrt{2}}$

$t=4$ days

$t_{1/2}=\frac{0.693}{K}$

$K=\frac{2.303}{4}log\sqrt{2}$

$K=0.086{days}^{+}$

$t_{1/2}=8.0days$

Case II $A=?$

$t=24$ days

$A_o=1gm$ } $\Rightarrow 0.086=\frac{2.303}{24}log\frac{1}{A}$

$A=0.126$ gm