Applying least squares to measurement of nuclei masses and Q-value

[schniefen]

Homework Statement

See attached image.

Relevant Equations

Q-value: The difference in mass between the mother atom and the daughter atom.

Consider the problem in the attached image. The difference between A and B is 0.0020(20). How does one use the least squares method, particularly in matrix form, to find the best value of the masses of A and B respectively, as well as the Q-value? Aren't more measurements needed for the masses and the Q-value?

 

[Steve4Physics]

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How does one use the least squares method, particularly in matrix form, to find the best value of the masses of A and B respectively, as well as the Q-value? Aren't more measurements needed for the masses and the Q-value?

View attachment 274740

Hi. Since no one has yet replied, I thought I’d chip in

Some clarification may be needed:

1) Why do you assume this is a ‘least squares’ question? The attachment mentions nothing about least squares.

2) The question ignores the mass of the emitted electron (assuming ${\beta}^-$ decay). This mass is about 0.0005u, so it is not negligible relative to the Q-value. (The anti-neutrino’s mass will be negligible though.) It is unclear whether or not the electron’s mass needs to be accounted for.

3) It is not clear (to me anyway) what the ‘matrix calculations’ might be. My gut feel is that the question is about some clever statistical method to reconcile partially consistent values. If so, ‘Introductory Physics Homework Help’ might not be the optimum place to ask. Can you provide some context? What course/level/topic is this from?

4) One minor point. Note that you have omitted units for the masses, and the attachment has omitted units for Q.

If you can clarify points 1-3, you might have a better chance of receiving some help.

Season's Greetings!