The time taken is 43.7 min
Step-by-step explanation:
The equation that describes the amount of mass left after a time t of a radioactive isotope is the following:
[tex]m(t) = m_0 (\frac{1}{2})^{\frac{t}{\tau}}[/tex]
where
[tex]m_0[/tex] is the mass of the sample at t = 0
[tex]\tau[/tex]is the half-life of the sample
For the element X in this problem,
[tex]\tau = 6 min[/tex]
[tex]m_0 = 310 g[/tex]
We want to find the time t at which
[tex]m(t)=2g[/tex]
So we need to re-arrange the equation making t the subject:
[tex]\frac{m(t)}{m_0}=(2)^{-\frac{t}{\tau}}\\t=-\tau log_2(\frac{m(t)}{m_0})=-(6)log_2(\frac{2}{310})=43.7 min[/tex]
Learn more about radioactive decay:
brainly.com/question/4207569
brainly.com/question/1695370
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