If a substance is radioactive, this means that the nucleus is unstabla and will

Question

If a substance is radioactive, this means that the nucleus is unstabla and will thenefore decay by any number of processes (alpha decay, beta docay, etc.). The decay of radioactive elements folows first-order kinetics. Therefore, the rate of decay can be described by the sarme integrated rate equations and ha-ife equations hat are uned so descrbe the rate of first-order chemical reattions Part c Americium-241 is used n some smoke detectors.is an abha emeer with a harste of 432 years. How long will it take in years for 43.0% of an Am-241 sample to decay? Express your answer with the appropriate units IA and 1/2 Value Units where Ao is the initial amount or activity, At is amount er activity at time t, and k is the rate constant thta My Answers Review Part By manipulation of these equations (substituting 0.693/t for & in the integrated rate equation), we can arrive at the following formula Part D Afossa was analysed and determined to have acarbon,14 level thatsS0%th old is the fossil? fraction remaining = = (0.5)" tofliving organism. The halute of C-14 is 5730 years. How where n is the number of half-ives. The equesion relating the number of hal -ives to timeis Express your answer with the appropriate units. where a is the length of one half-ife tValue Units Hiets My Answers Give Up Review Part Continue

Explanation / Answer

partC

K = 0.693/t1/2
given
   t1/2 = 432 years
K = 0.693/432
K = 1.604*10^-3 year^-1

we know

   K = 2.303/t log(initial/final)
   1.604*10^-3 = 2.303/t log[100/(100-43)]
     t = 0.562/1.604*10^-3
     t = 350.51 years.
the time taken to complete 43% of decay is 350.51 years

PartD

t = [2.303log(N/N0)/(-0.693)]*t1/2
t = [2.303log(50/100)/(-0.693)]*5730
t = [2.303*0.3010/0.693]*5730

t = 5730 years old

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