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Radioactive decay can be described by the following equation In A = In A_0 -kt Where A_0 is the original amount of the substance, A is the amount of the substance remaining after time t, and k is a constant that is characteristic of the substance. For the radioactive isotope lead -214, k is 2.59 times 10^-2 minutes^-1 If the original amount of lead - 214 in a sample is 25.9 mg, how much lead-214 remains after 29.7 minutes have passed?

Respuesta :

Answer: The amount of lead-214 remaining after given time is 12 mg.

Explanation:

The equation used to calculate the amount of sample for first order kinetics follows:

[tex]\ln A=\ln A_o-kt[/tex]

where,

[tex]A_o[/tex] = initial mass of isotope = 25.9 mg

N = mass of the isotope left after the time = ? mg

t = time = 29.7 min

k = rate constant = [tex]2.59\times 10^{-2}min^{-1}[/tex]

Putting values in above equation, we get:

[tex]\ln A=\ln (25.9mg)-(2.59\times 10^{-2}min^{-1}\times 29.7min)\\\\A=12mg[/tex]

Hence, the amount of lead-214 remaining after given time is 12 mg.

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