Question

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?

Answer 1

the answer is A.46 Million years

Answer 2

t = 45.5 million years

Step-by-step explanation:

Initially whole sample is consisting the radioisotope

so initial total mass will be

`m_0 = 16.75 g + 50.25 g`

`m_0 = 67 g`

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

`m = 16.75 g`

now we also know that half life is 23 million years

so we have

`m = m_0 e^(-\lambda t)`

now we have

`16.75 = 67e^(-\lambda t)`

`0.254 = e^(-\lambda t)`

`\lambda t = 1.37`

`(ln 2)/(23 million \:years) t = 1.37`

t = 45.5 million years

so above is the time interval