If one half-life of U-236 is 23 million years then it will take 45.5 or approximately 46 million years to decay. Then the correct option is A.
Half-life is the time interval that is needed to decay the atomic nuclei of a radioactive sample.
A sample contains 16.75 g of the radioisotope U-236 and 50.25 g of its daughter isotope, Th-232.
Initially, the whole sample is consisting the radioisotope. Then the initial total mass will be
m₀ = 16.75 + 50.25
m₀ = 67 g
Now we also know that the half-life is 23 million years. Then we have
[tex]m = m_oe^{- \lambda t}[/tex]
Then put the value
[tex]\begin{aligned} 16.75 &= 67 e^{- \lambda t}\\\\0.254 &= e^{- \lambda t}\\\\\lambda t &= 1.37\\\\\dfrac{ln2}{23 \rm \ million \ years } \times t &= 1.37\\\\t &= 45.5 \ \rm million\ years \end{aligned}[/tex]
If one half-life of U-236 is 23 million years then it will take 45.5 or approximately 46 million years to decay. Then the correct option is A.
More about the half-life link is given below.
https://brainly.com/question/24710827
