Answer to Question #167215 in General Chemistry for koo

Question

1) 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.

2) Phosphorus-32 is used in biochemical studies to follow the pathway taken by metabolites. Its half-life is 14.3 days. A vial containing 10μg of P-32 is accidentally spilled into a sink.
a) How long will it take P-32 in the drain to exhibit 65% of its original activity?
b) How many atoms of P-32 remain in the sink after 785 days?

Answer 1

The radioactive nuclei all obey the primary kinetics, which explicitly proportionate to the number of nuclei present to the decline rate of the radioactive nuclei. This partnership can be written as:

$rate=k[N]\ where,$

k is the rate constant and N is the number of radioactive nuclei.

$k=\dfrac{0.693}{t_{1/2}}=\dfrac{0.693}{36hrs}$

$=0.01925hr^{-1}$

$N_0=\dfrac{1.4*10^5 disintegration}{60min}$

$k=\dfrac{2.303}{t}log\dfrac{N_0}{N_t}$

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

 $=Antilog0.3009=1.999=2$

$N_o=N_t\times{2}=\dfrac{1.4\times 10^5\times 2}{60}=\dfrac{4.66*10^3 disintegration}{1hr}$

Grams present in the sample

 $N_t-No=(4.66-2.33)\times 10^3=2.33\times 10^3$

=$\dfrac{2.33}{4.66}\times 100=50$ %

 $Br-82=100-\dfrac{50}{100}(82)\newline=82-41=41g$