Bismuth?214 can undergo both an alpha decay and a beta decay. Complete the react

Question

Bismuth?214 can undergo both an alpha decay and a beta decay. Complete the reactions below.

(a) 214/83Bi --Alpha Decay-->__________ + ________________

(b) 214/83Bi --Beta Decay--> ___________ + _________________

(c) Predict the missing species in this nuclear reaction: 75/35Bi --> 0/-1Beta + ________

(d) A patient is given a 58.0?mg dose of Iodine?131 to image the thyroid. This nuclide has half life = 8.0 days. What mass of the nuclide remains in the patient after 33.0 hours, when the thyroid scan is taken? (hint: nuclear decay reactions are 1st order kinetics.)

Explanation / Answer

Alpha decay involves the creation of a helium atom and the new atom which conserves mass

214/83Bi --> 4/2He + 210/81 Tl (Thallium)

Beta decay involves the creation of a proton and electron from a neutron

214/83Bi --> 0/-1β + 214/84 Po (Polonium)

c) Just want to point out that the species in this question is not bismuth but bromine, because it has atomic number 35, but...

75/35Br --> 0/-1β + 75/36Kr

d) Because we know that this is a first order kinetic reaction and that the half life is 8 days, we can find the rate constant using the following equation and rearranging for k

half life = ln 2/k --> k = ln 2/half life = 0.693/8.0 = 0.086625

Now we can use the integrated rate law reaction:

[A]t = -kt + [A]0 where [A]t is the concentration we're looking for, and [A]0 is the initial concentration.

Note that we don't need to convert the masses into concentrations because we would have to do the same operations to both masses and it would change nothing. Not only that, but we need to final concentration in grams, so it would be a bit of a hassle to convert there and then convert back.

[A]t = -(0.086625 days^-1)(33 hours/24 hours/day) + 58 mg of I = 57.88 mg

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