The half-life period of a radioactive element is 7 days. The fraction of the radioactive element that disintegrates in 21 days is 0.406.
The half-life period of a radioactive element is 7 days.
Fraction of the sample will remain after 21 days:
The decay constant [tex]\lambda[/tex] = [tex]\frac{0.693}{t_{1/2} }[/tex]
= [tex]\frac{0.693}{7} = 0.099[/tex]/ hour
t = 21 days
t = [tex]\frac{2.303}{\lambda} log\frac{a}{a-x}[/tex]
21 = [tex]\frac{2.303}{0.099}log\frac{a}{a-x}[/tex]
0.9028 = [tex]log\frac{a}{a-x}[/tex]
2.466 = [tex]\frac{a}{a-x}[/tex]
[tex]\frac{a-x}{a} =0.406[/tex]
Hence,
The half-life period of a radioactive element is 7 days. The fraction of the radioactive element that disintegrates in 21 days is 0.406.
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