What is the definition of the dalton (Da) unit?

[heroslayer99]

Homework Statement

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Relevant Equations

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I am very confused with this question, firstly, I am unsure what is meant by the "unified atomic mass unit" I know that it is defined as "1/12 of the mass of an atom of carbon 12", but this sounds like it takes into account the electrons, i.e that is this means to me that unified atomic mass unit = mass of 6 electrons in c12 + mass of nucleus / 12" but then surely the rest mass of a proton would be more than the atomic unit, but we all know that the rest mass of a proton is slightly more than the unified atomic unit. Also carbon 12's nucleus has a mass of exactly 12 unified atomic units, indicating that the definition of "unified atomic mass unit" should really be "1/12 of the mass of a nucleus of carbon 12". I would like some further clarification on this.

 

[Orodruin]

This is from the SI definition.

that is this means to me that unified atomic mass unit = mass of 6 electrons in c12 + mass of nucleus / 12"

No. You are forgetting about binding energy.

The proton has a mass larger that 1 amu because a C-12 nucleus has less mass than 6 protons and 6 neutrons.

 

[heroslayer99]

I see, so the nucleons lose some mass which is converted into energy and therefore the nucleus is held together albeit with less mass than the sum of its constituents. Does amu still take the electrons into account?

 

[heroslayer99]

I can see online that apparently the mass of an atom of c12 is 12amu and the mass of a nucleus of an atom is 12amu, clearly both cannot be true.

 

[Orodruin]

I can see online that apparently the mass of an atom of c12 is 12amu and the mass of a nucleus of an atom is 12amu, clearly both cannot be true.

Please provide references. Saying you saw something somewhere does nothing for the discussion.

I see, so the nucleons lose some mass which is converted into energy and therefore the nucleus is held together albeit with less mass than the sum of its constituents. Does amu still take the electrons into account?

No. The nucleons themselves do not lose mass. The system as a whole has less energy - and therefore less mass - than the nucleons do when separated.

 

[jbriggs444]

Please provide references. Saying you saw something somewhere does nothing for the discussion.


No. The nucleons themselves do not lose mass. The system as a whole has less energy - and therefore less mass - than the nucleons do when separated.

With a little Google foo, I found an article which appears to explain things nicely. As an added bonus, it provides a link to a reference with the false claim in question.

The mass of the nucleus of a carbon atom is exactly
(12 daltons) −−
(
(6 × (the mass of an electron)) −−
(their binding energy [converted to mass])
).
The mass of an electron is $5.486 \times 10^{−4}$ daltons. The electrons’ binding energy will be a few tens of electron-volts. Since an electron-volt is around $10^{−15}$ daltons, that component of the mass is buried in the imprecision of the following result. Thus, the mass of a carbon-12 nucleus works out to 11.9967084 daltons.
However, many sources state that the nucleus of carbon-12 has a mass of exactly 12 daltons. For example, one article, Carbon-12 - Wikipedia, contains both these contradictory statements, with no recognition of its own self-contradiction. I am unable to find any direct statement of the mass of a carbon-12 nucleus other than the incorrect 12 daltons. For that reason, one must state carefully the mass that one is using in any calculations, and one must distrust published works involving the mass of the carbon-12 nucleus.

I chased the link in the above but could not find a claim there about the mass of the Carbon-12 nucleus alone.

 

[heroslayer99]

From what I can gather the electrons are taken into account when calculating amu. Finally I have one more question, In the following question the author subtracts the mass of the alpha particle from the uranium nucleus, to get the mass of the thorium nucleus. Is the author just blatantly ignoring the fact that the energy given out to the two products must come from a loss in mass of the system, which implies the sum of the masses is not constant on both sides of the equation (so you cannot simply subtract one from the other)?

 

[jbriggs444]

The binding energy here is small compared to the masses of either of the daughter particles. At the level of precision (two sig figs) here, it is negligible.

 

[heroslayer99]

If you saw this question on a test, what hints you towards ignoring the binding energy?

 

[Steve4Physics]

If you saw this question on a test, what hints you towards ignoring the binding energy?

Be aware that allowing for nuclear binding energies will change calculated masses by less than 1%.

You can usually spot questions where binding energy needs to be taken into account because values of mass will be given to a fairly large number (e.g. 6) of significant figures.

Also, the nature/context of the question should guide you.

By the way, 'amu' is a bit outdated. A single 'u' is often used. But to be up to date, the name for this unit is the dalton (symbol Da).

 

[heroslayer99]

Be aware that allowing for nuclear binding energies will change calculated masses by less than 1%.

You can usually spot questions where binding energy needs to be taken into account because values of mass will be given to a fairly large number (e.g. 6) of significant figures.

Also, the nature/context of the question should guide you.

By the way, 'amu' is a bit outdated. A single 'u' is often used. But to be up to date, the name for this unit is the dalton (symbol Da).

Thank you!!!!!