Question #163810

Bromine-82 has a half-life of 36 hours. A sample containing Br-82 was found to have an activity of

1.4 x 105 disintegrations/min. How many grams of Br-82 were present in the sample? Assume that

there were no other radioactive nuclides in the sample.

Expert's answer

As we know,

Decay constant, "k =\\dfrac{0.693}{t_{\\frac{1}{2}}}=\\dfrac{0.693}{36\\text{hour}}=0.01925hr^{\u22121}"

"N_o=1.4\\times 10^5\\text{disintegration\/min}=\\dfrac{1.4}{60}\\times 10^5{\\text{disintegration\/hour}}"

Also,

"k=\\dfrac{2.303}{t}log\\dfrac{N_0}{N_t},"

"log\\dfrac{N_0}{N_t}=\\dfrac{kt}{2.303}=\\dfrac{0.01925\\times 36}{2.303}=0.3009"

or "\\dfrac{N_0}{N_t}=Antilog0.3009=1.999=2"

"N_o=N_t\\times{2}=\\dfrac{1.4\\times 10^5\\times 2}{60}=4.66\\times10^3\\text{disintegration\/hour}"

Grams of Br-82 present in the sample is "N_t-No=(4.66-2.33)\\times 10^3=2.33\\times 10^3"

="\\dfrac{2.33}{4.66}\\times 100=50" %

Grams of "Br-82=100-\\dfrac{50}{100}(82)=82-41=41g"

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