# Q-value in beta minus decay does not match.

## Main Question or Discussion Point

Hi

I'm wondering if someone could help me out finding the Q-value fom a beta minus decay.

It's a
90Y → 90Zr + e

All sources I have says that the energy released is 2,28 MeV, but when i calculate i get 1,78 MeV

So far, I've looked up the mass of the 90Y and the Zr90 and the electron and done following:

Q=(m(90Y)-m(90Zr)-m(e))*c^2

According to my databook

m(90y) = 89,9071519u = 1,49294*10^-25 kg
m(90Zr) = 89,9047044u = 1,4929*10^-25 kg
m(e) = 9,10938*10^-31 kg

Giving a mass difference at 3,15323*10^-30 kg

resulting in a Q value of Q=2,83399*10^-13 J = 1,76883 MeV

If you can tell me what im doing wrong, I would appreciate if you would let me know.

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Bill_K
I would just point out that the difference between your answer and the expected answer is about 0.5 MeV, i.e. the mass of the electron.

jtbell
Mentor
Hint: isotopic mass tables list the masses of complete atoms (including electrons), not bare nuclei.

I finally got the right result!

Thanks a lot :)

I tried only calculation with masses of the mother- and the daugther nucleus, without the β particle itself, and that gave me the 2,28 MeV i was looking for.

But, I'm still confused. How can i get it right, when im ignoring a product? if
Q = (m(product) - m(reactants) )*c^2

Am i just allowed to ignore the elektron?
Or is the electron actually a part of the daughter nucleus as n→p+e?

Bill_K
Is it really the case that people calculate their nuclear reactions nowadays in terms of Joules and Kilograms?

jtbell
Mentor
Hint: isotopic mass tables list the masses of complete atoms (including electrons), not bare nuclei.
Hint #2: How many electrons does a Y atom have, and how many electrons does a Zr atom have?

My teacher prefer that we use SI-Units, as we will be sure that the results are in SI-Units.
Also, I don't know what county the majority of the users of this forum is, but I live in Denmark, and here we use the metric system (Don't know if that even matters here).

The Y has 39, and the Zr has 40. Is the extra electron from the Zr the β? If so, how is the Zr atom stable?

PAllen
2019 Award
My teacher prefer that we use SI-Units, as we will be sure that the results are in SI-Units.
Also, I don't know what county the majority of the users of this forum is, but I live in Denmark, and here we use the metric system (Don't know if that even matters here).

The Y has 39, and the Zr has 40. Is the extra electron from the Zr the β? If so, how is the Zr atom stable?
1) What Bill_K is referring to is that nuclear reactions (in my experience, and apparently his) are computed using amu and mev directly. Going to joules and kilograms seems lunatic.

2) Do you think, when Y decays by beta, and emits a high energy electron which escapes, the result is a neutral Zr or an ionized Zr? Account for this and all will balance.

Meir Achuz