Radioactive Decay Calculation

[Millano]

Homework Statement

A sample of pure 99mTc is obtained and has an activity of 5000MBq. What will be the approximate change in mass of this sample after it has all decayed to 99Tc (assume no further decay from this state).
(Avogadro's number = 6.023x1023 per mole; Half life of 99mTc = 6Hrs. Assume all 99mTc decays by the emission of 140keV gamma rays )

Homework Equations

N/N0 = e-zt,

halflife= ln2/z
A= zN
N*mass number/avogado number = mass of nuclei
z=decay constant
N= number of atoms remaining
A= activity

The Attempt at a Solution

Used halflife= ln2/z to work out the decay constant = 3.2 * 10^-5
A/z= N so, 5*10^9/3.2 * 10^-5 = 1.56*10^14 = N

Dont know if this is correct or what to do from here... thanks.

 

[anathema]

I would like to clarify a few things before providing an answer to this question. Firstly, the given information about the half-life of 99mTc and the emission of 140keV gamma rays is correct. However, the activity of the sample is not measured in MBq (megabecquerel) but in Bq (becquerel). 1 MBq = 10^6 Bq. So, the activity of the sample is actually 5*10^9 Bq.

Now, to answer the question, we need to understand the concept of radioactive decay. When a radioactive nucleus decays, it emits radiation and transforms into a different nucleus. This process continues until the nucleus reaches a stable state. In this case, 99mTc decays to 99Tc by emitting a gamma ray with energy of 140keV. This process continues until all 99mTc nuclei have decayed to 99Tc.

The key concept to keep in mind here is that the number of atoms (or nuclei) in a sample remains constant throughout the decay process. This means that even though the nuclei are decaying, the total number of atoms remains the same. So, the number of 99Tc nuclei will be the same as the number of 99mTc nuclei initially present in the sample.

To calculate the number of 99Tc nuclei present in the sample, we can use the equation N = N0*e^(-λt), where N is the number of nuclei remaining, N0 is the initial number of nuclei, λ is the decay constant, and t is the time. Using the given information, we can calculate the decay constant as 3.2*10^-5. The time, t, can be calculated by using the half-life equation, t = (ln2)/λ, which gives us t = 21.66 hours.

Substituting these values in the above equation, we get N = 5*10^9*e^(-3.2*10^-5*21.66) = 1.56*10^14 nuclei of 99Tc.

Now, to calculate the change in mass, we need to use the equation A = zN, where A is the activity, z is the decay constant, and N is the number of nuclei. The activity of 99Tc can be calculated by multiplying the decay