From: Ronald Wong (ronwong@inreach.com)
Date: Tue Oct 31 2000 - 17:05:34 PST
Message-Id: <l03102804b624fd0a3a33@[209.209.20.24]> Date: Tue, 31 Oct 2000 17:05:34 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re: the mass and the mass number
Camille followed up my response to her post on C-12 with a couple of
questions addressed to me and I thought the answers m..i..g..h..t be of
interest to others:
------------------------------------
>One additional question: why are the masses of some isotopes (like those of
>Li) greater than their mass numbers?
The mass number is just the closest integer to the atomic mass of the
nuclei. Since the mass of the proton and neutron are a little greater than
one, it isn't surprising that the atomic masses are usually greater than
their mass number.
If you check the numbers out, you'll find that this is generally the case
for the majority of the isotopes. (The real question is why are there cases
where "...the mass of some isotopes" is LESS than the mass number?)
Regarding your second question:
>Don't all nuclei require some binding energy?
One of the discoveries made in the earlier part of the last century was
that when you add up the mass of all the protons and neutrons that have
come together to make up the nucleus of an isotope, you'll ALWAYS end up
with a sum that is greater than the atomic mass of the isotope.
The difference between the sum and the actual atomic mass of the nucleus is
a function of how much energy went into holding all of the nucleons
together in the atom. It's the old E = mc^2 business - where the mass
difference represents the "m" in the formula. In the MKS system of
measurement this would be in kilograms (1 u is about 1.66X10^-27 kg).
So, since the sum will ALWAYS be greater than the whole - the difference
reflecting the amount of binding energy, the answer to your second question
is yes.
Finally, the answer to my question:
So how is it possible for the sum to be less than the mass number? Well,
the sum is still greater than the atomic mass but the atomic mass of some
isotopes is in fact less than their atomic number (that is, it is just a
little less than a whole number). Apparently, the numbers just work out
that way - and that should be enough to satisfy the curiosity of your
students. In reality, there is more going on here, but the explanation can
be a little tedious - well....not for a REAL physicist (...well maybe for
some of them too).
ron
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