The half-life of phosphorous -32 is 14 days.
Half-life:
The period of time it takes for 50% of a radioactive substance's atoms to disintegrate.
How to calculate the half-life?
[tex]T= \frac{ln[2]}{A}[/tex]
Mass of atoms initially, [tex]$N_{0}=2.0 \mathrm{~g}$[/tex]
Mass after 42 days, [tex]$N=0.25 \mathrm{~g}[/tex].
Mass left undecayed we have,
[tex]$\frac{N}{N_{0}}=\frac{1}{2^{n}}$[/tex]
where [tex]$n$[/tex] is number of half lives occured
[tex]$\begin{aligned}&\Rightarrow \frac{0.25}{2}=\frac{1}{2^{n}} \\&\Rightarrow \frac{1}{8}=\frac{1}{2^{n}} \\&\Rightarrow n=3\end{aligned}$[/tex]
Number of half lives occured in 42 days is 3
if half life is [tex]$t_{\frac{1}{2}}$[/tex]
then [tex]$3 t_{\frac{1}{2}}=42$[/tex]
or
[tex]$t_{\frac{1}{2}}=14$[/tex]
[tex]$\therefore$[/tex]half life is of 14 days.
Therefore, The half-life of phosphorous -32 is 14 days.
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