1. Iodine-131, t(1/2)= 8.0 days, is used in diagnosis and treatment of thyroid g

Question

1. Iodine-131, t(1/2)= 8.0 days, is used in diagnosis and treatment of thyroid gland diseases. If a laboratory sample of Iodine-131 initially emits 9.95E18 beta particles per day, how long will it take for the activity to drop to 6.22E17 particles per day? (The answer is supposed to be 32 days.)

2. It is believed that two carbon-12 nuclei can react in the core of a supergiant star to form sodium-23 and hydrogen-1. Calculate the energy released from this reaction for each mole of hydrogen formed. The masses of carbon-12. sodium-23, and hydrogen-1 are 12.0000 amu, 22.989767 amu, and 1.007825 amu, respectively. (The answer is supposed to be 2.16E11 kJ/mol H.)

Please show all calculations/work, thank you. The answers were provided by the professor, but I am confused as how to even approach these problems.

Explanation / Answer

(1) All radio active decay are first order reactions only.

so, k = 0.693 / t1/2

k = 0.693 / 8 = 0.086625 per day

And we know that first order rate integration equation as,

k = 2.303 Log[initial/final] / t

0.086625 = 2.303 Log[9.95*1018/6.22*1017] / t

t = 32 days

(2) Mass change = 2(12.0000) - 22.989767 - 1.007825 = 0.002408 amu = 0.002408*1.66*10-27 kg

= 0.00399728*10-27 kg/atom

= 0.00399728*10-27 *6.022*1023 kg/mol

= 0.024072 *10-4kg/mol

Energy change = mass change * c2

= 0.024072*10-4*(3*108)2

= 2.166*1011 kJ/mol

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