Rate constant for the decay of bromine-87?

Question

Full problem: The number of undecayed nuclei in a sample of bromine-87 decreased by a factor of 4 over a period of 112 sec. What is the rate constant for the decay of bromine-87?

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an explanation of your approach to the problem would be appreciated.

thanks so much!

Answer 1

Half-life is 56 seconds.  Every 56 seconds, half of bromine-87 disappears.  

Answer 2

It decreased by a factor of 4 in two half-lifes; reduced to half in one half-life, and that remainder is halved (to a quarter) in another half-life.

Half-life = 112/2 = 56 sec.

The decay constant = 0.693/half-life = 0.0124 sec^(-1).

Do you need the derivation of the formula, decay constant = 0.693/half-life ?