Problem: The nuclide 96Nb decays by a first-order process with a rate constant of 2.96×10–2 min-1. How long will it take for 26.0% of the initial amount of 96Nb to be consumed?A) 44.0 hB) 0.170 hC) 27.7 hD) 6.70 hE) 0.758 h

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We’re being asked to determine the time it will take for 26.0% of the initial amount of 96Nb to be consumed.


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:

ln [N]t=-kt+ln [N]0

where:

[N]t = concentration at time t
k = decay constant
t = time
[N]0 = initial concentration

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Problem Details

The nuclide 96Nb decays by a first-order process with a rate constant of 2.96×10–2 min-1. How long will it take for 26.0% of the initial amount of 96Nb to be consumed?

A) 44.0 h

B) 0.170 h

C) 27.7 h

D) 6.70 h

E) 0.758 h