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A sample contains 16.75 g of of the radioisotope U-236 and 50.25 g of its daughter isotope , Th-232. how long did it take for decay to take place of one half-life of U-236 Is 23 million years?

Respuesta :

the answer is A.46 Million years

Answer:

t = 45.5 million years

Explanation:

Initially whole sample is consisting the radioisotope

so initial total mass will be

[tex]m_0 = 16.75 g + 50.25 g[/tex]

[tex]m_0 = 67 g[/tex]

now after some time we can say the radioactive nuclei is of mass

[tex]m = 16.75 g[/tex]

now we also know that half life is 23 million years

so we have

[tex]m = m_0 e^{-\lambda t}[/tex]

now we have

[tex]16.75 = 67e^{-\lambda t}[/tex]

[tex]0.254 = e^{-\lambda t}[/tex]

[tex]\lambda t = 1.37[/tex]

[tex]\frac{ln 2}{23 million \:years} t = 1.37[/tex]

t = 45.5 million years

so above is the time interval

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