Answer:
Ending Amount = beginning amount / 2^n where "n" is the number of half-lives or elapsed time / half-life
For this problem "n" = 25 / 11 = 2.2727272727
Ending Amount = 60 grams / 2^2.2727272
Ending Amount = 60 / 4.832357534
Ending Amount = 12.4162998242 grams
Source: www.1728.org/halflife.htm
Step-by-step explanation:
A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. The element would remain after 25 years, to the nearest whole number is 2 grams.
A radionuclide is a nuclide with excessive nuclear energy, which makes it unstable. This surplus energy can be discharged as gamma radiation from the nucleus, transferred to one of its electrons and released as a conversion electron, or used to generate and produce a new particle from the nucleus.
Given the life of radioactive material is stated by the formula,
[tex]N_t = N_o e^{-\lambda t}[/tex]
Now, given the half-life of the comes in 11 years, therefore, the rate of decay will be,
[tex]N_t = N_o e^{-\lambda t}\\\\\dfrac{N_t}{ N_o }=e^{-\lambda t}\\\\0.5 = e^{-\lambda \times 11}\\\\\dfrac{ln(0.5)}{11}=\lambda[/tex]
λ = 0.14631
Given the initial mass is 60 grams, therefore, the amount that will be remaining after 25 years will be,
[tex]N_{25} = 60 \times e^{(-0.14631\times 25)}\\\\N = 1.5474\rm\ grams \approx 2\ grams[/tex]
Hence, the element would remain after 25 years, to the nearest whole number is 2 grams.
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