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Element X decays radioactively with a half life of 6 minutes. If there are 970 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 139 grams?
y = a(.5) *

Respuesta :

Answer: 16.81 min

Step-by-step explanation:

Given

Initial concentration [tex]A_o=970\ gm[/tex]

Half-time  [tex]T_{\frac{1}{2}}=6\ min[/tex]

Decay at any time t is given by

[tex]A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}[/tex]

put values

[tex]\Rightarrow 139=970\cdot 2^{\dfrac{-t}{6}}\\\\\Rightarrow 2^{\dfrac{t}{6}}=6.978\\[/tex]

Taking log both sides

[tex]\Rightarrow \dfrac{t}{6}\times \ln (2)=\ln (6.978)\\\\\Rightarrow t=6\times 2.802\\\Rightarrow t=16.81\ \text{min}[/tex]

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