Nuclear Decay Scheme: Learn the Basics

In summary, the conversation discusses how to calculate the amount of Mo needed six hours earlier to produce 20MBq of Tc99m, taking into account a yield of 85%. There is a potential mistake in the question as it does not specify which form of technetium is being referred to, leading to confusion. The suggested approach is to calculate the number of atoms of Tc99m with an activity of 20MBq, rather than the activity of 30 Bq as stated in the question. Additionally, the correct spelling and pronunciation of the Greek letter ##\lambda## is mentioned.
  • #1
Benlaww
18
3
Homework Statement
Using a simplified decay scheme for the generator (shown in attempt of solution box) and assuming that initially only 99Mo is present, the number of 99Tc atoms N_Tc as a
function of time t is given by:
N_Tc(t) = (landa_Mo/(landa_Tc - landa_Mo))*N_Mo(0)*(e^(-landa_Mo*t) - e^(-landa_Tc*t))

Calculate the minimum activity of 99Mo required to produce 20 MBq of 99Tc at t
= 6 hours. State clearly any assumptions you make
Relevant Equations
A=landa*N
tc.JPG
I'm not too sure where to start, do I differentiate the equation?
 
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  • #2
Benlaww said:
I'm not too sure where to start, do I differentiate the equation?
You can just calculate how much Tc99m has an acitivity of 30 Bq, and then use the equation to calculate how much Mo you need six hours earlier. The only thing not accounted for in the equation is the yield of 85% Tc99m.
I'm sure you can ignore the decay of the ordinary Tc99,
 
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  • #3
There's a mistake/ambiguity in the question which could cause confusion. There are 2 different forms of technetium referred to in this question but the question doesn't distinguish between them.

99Mo decays either to 99mTc (the metastable form) or to 99Tc.

Neither the diagram nor the question mention 99mTc but it appears you are actually being asked how many atoms of 99Mo were needed to produce 20MBq of 99mTc (not 20MBq of 99Tc).

I agree with @willem2's approach, except that I presume
"how much Tc99m has an acitivity of 30 Bq"
should really be
"how many atoms of Tc99m have an acitivity of 20MBq ".

Also, for information, the English-equivalent spelling of the Greek lettter ##\lambda## is ‘lambda’. It is pronounced ‘lam-da’. (Not to be confused with the dance the 'lambada' as some of my students did many years ago!).
 
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What is nuclear decay?

Nuclear decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, resulting in the formation of a more stable nucleus.

What are the different types of nuclear decay?

The three main types of nuclear decay are alpha decay, beta decay, and gamma decay. In alpha decay, an alpha particle (consisting of two protons and two neutrons) is emitted from the nucleus. In beta decay, a beta particle (either an electron or a positron) is emitted from the nucleus. In gamma decay, a high-energy photon is emitted from the nucleus.

What is a nuclear decay scheme?

A nuclear decay scheme is a graphical representation of the sequence of nuclear decays that occur in a radioactive sample. It shows the type of decay, the energy of the emitted particle or photon, and the resulting nucleus at each step.

How is the stability of a nucleus determined?

The stability of a nucleus is determined by the ratio of protons to neutrons. If this ratio is too high or too low, the nucleus will be unstable and undergo nuclear decay in order to reach a more stable state. This is known as the neutron-to-proton ratio.

Why is understanding nuclear decay important?

Understanding nuclear decay is important for a variety of reasons. It helps us understand the behavior of radioactive materials and their potential effects on the environment and human health. It is also crucial in fields such as nuclear energy, nuclear medicine, and carbon dating. Additionally, studying nuclear decay can provide insights into the fundamental forces and processes that govern the behavior of matter at the atomic level.

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