FQ2Q - Mass Defect of a Nucleus (1 Viewer)

[Antisocial]

I've asked the teacher about this after I made a big fuss about it during class (my identity is now revealed to some, no doubt) and he said he'd come up with an answer but... that didn't exactly happen.

The Jacaranda textbook gives an example for working out mass defect of a deuterium nucleus:
The mass of a deuterium atom is 2.014102 u. Therefore, there mass of a deuterium nucleus is 2.014102 - 0.000549 = 2.013553 u (mass of atom - mass of electron). The total mass of an isolated proton and neutron would be 2.015941 u. If this proton and neutron combined to form a deuterium nucleus, they would have to lose 2.015941 - 2.013553 = 0.002388 u. And that is the mass defect.

Right.

Now, in another worked example the book gives...
The mass of a helium atom is 4.002603 u.
Calculate the mass defect of the helium nucleus.

The total mass of the constituents of a helium atom (2 protons, 2 neutrons, 2 electrons) is: 2 (1.007276 + 1.008665 + 0.000549) = 4.032980 u.
Mass defect
= 4.032980 - 4.002603
= 0.030377 u.

That's where I'm confused. Why is it in example 1, the mass of the electrons is subtracted from the total mass of the atom to find the mass defect of the nucleus (which I think makes more sense...) whereas in example 2, they subtracted the mass of the atom from the total mass of its constituents to find the mass defect of the nucleus?

Thanks in advance for taking time to read such a long-winded query when the answer is probably so blatantly obvious.

 

[jims]

im not sure if id be answering ur question (which im uncertain of anyway).
anyway, in ex1 theyve just subtracted the electrons to find the mass of the nucleus. they could have left the mass of the electron in there and added it to the proton and neutron to get the same answer. ie p + n + e = 2.015941 (p + n) + 0.000549 (e) = 2.016490
then the mass defect = 2.016490 - 2.014102 = 0.002388 u which is the same answer ex1 had. this is the way they did it in ex2. so in ex2, u could have subtracted the 2 e from the mass of the helium atom and then subtacted that from the mass of the 2 p and 2 n (which is exactly the same thing but done differently).

edit: beat the person below by less than a minute haha

while im editing, this is something i should have included:
mass defect = mass of atom - mass of constituents
i think this is more clearly down in ex2, but if u like ex1 then do it that way.

 

[Mathematician]

...

And it is. The fact that u could think its obvious is probably cause ur subconscious already knows why but ur concious insists on it now.. Anywayz

What u really wanna know is why the mass defect is told as

(1) The difference between the mass of the constituent particles of a nucleus(which are the protons and neutrons) when they are alone and the mass of the nucleus ( mass of constituent particles when in the nucleus being the protons and neutrons ).

But then also told as:

(2) The difference between the mass of the constituent particles of an atom(which are the protons,neutrons and electrons) when they are alone and the mass of the atom ( mass of constituent particles when in the atom being the protons, neutrons and electrons).

Which is faster if one wishes to calculate the mass deffect since the mass of an atom is known straight from the periodic table.

Lets start with (2).

FIRST THAT U MUST ACCEPT THAT THE ELECTRON'S MASS IS ALWAYS THE SAME AS IT CAN NEVER BE IN THE NUCLEUS. IN OTHER WORDS IT IS ALWAYS "FREE"

Mass Defect = Mass of const.. of atom - Mass of atom =
(Mass of protons and neutrons + Mass of electron) - (Mass of nucleus + electron) = (Mass of protons and neutrons) - (Mass of nucleus) = Mass of const.. of nucleus - Mass of nucleus

This is (1)
So they are really both the same thing mathematically. I would say the real definition is (1) but (2) yields the same result.

Hope that helped and answered the Question.

 

[Mathematician]

..

I knew i was taking too long.

What a waste of time. It better have helped. But jims is right saying it in a quick way, unlike me

 

[Antisocial]

Re: ...

Thanks to both of you, and Mathematician is right.

Originally posted by Mathematician
And it is. The fact that u could think its obvious is probably cause ur subconscious already knows why but ur concious insists on it now..

If I went over this over month ago, I wouldn't have had a problem, but this time I'd stuffed up my calculations because when I tried to do example 1 using example 2's method, I got the same answer whereas when I tried to do example 2 using example 1's method, I got a slightly different answer (by 0.00004, or thereabouts) and became even more confused.