The fraction of radioisotope left after 1 day is [tex](\frac{1}{2})^{\frac{1}{\tau}}[/tex], with the half-life expressed in days
Explanation:
The question is incomplete: however, we can still answer as follows.
The mass of a radioactive sample after a time t is given by the equation:
[tex]m(t)=m_0 (\frac{1}{2})^{\frac{t}{\tau}}[/tex]
where:
[tex]m_0[/tex] is the mass of the radioactive sample at t = 0
[tex]\tau[/tex] is the half-life of the sample
This means that the mass of the sample halves after one half-life.
We can rewrite the equation as
[tex]\frac{m(t)}{m_0}=(\frac{1}{2})^{\frac{t}{\tau}}[/tex]
And the term on the left represents the fraction of the radioisotope left after a certain time t.
Therefore, after t = 1 days, the fraction of radioisotope left in the body is
[tex]\frac{m(1)}{m_0}=(\frac{1}{2})^{\frac{1}{\tau}}[/tex]
where the half-life [tex]\tau[/tex] must be expressed in days in order to match the units.
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