Practice Problems Week 10

1. Write balanced nuclear equations for the following:

(a)    : ²¹⁴Pb -> ²¹⁴Bi + ⁰b

(b)   : ²³¹Pa ->²²⁷Ac + ⁴a

(c)   

(d)  

(e)   

(f)    

(g)   

2. Iodine-134 has a half-life of 52.0 minutes. If you begin with 1.28 mg of the isotope, how much is left after 0.289 days?

            Well, the half-life is given in minutes, so let’s convert 0.289 days into minutes:

Now! How many times will 52.0 minutes/half-life go into 416 minutes?

So, we know that

3. A 64.0 mg sample of ²³⁵Pu decays to 2.00 mg in 130 minutes. What is the half-life of this isotope?

So, what fraction of the initial mass 64.0 mg is 2.00 mg? It’s 2.00/64.0 or 1.00/32.0. But 1.00/32.0 is 1.00/(2.00)5. So it has been divided by two, five times, meaning the time span of five half-lives has passed. So, if 130 minutes is five half-lives, then one half-life is

.

4. How many weeks have passed if a 32.0 mg sample of a radioactive nuclide has decayed to 2.00 mg?    (t_½ = 6.5 days)

             The basic question here is: “How many times has the mass been divided by two?” That would be the number of half-lives. Then we multiply that number by 6.5 days and convert to weeks:

So we have four half-lives each at 6.5 days making 26 days or 3.7 weeks.