How Do You Calculate the Mass of an Isotope?

[enternaL]

I'm trying to find the mass of a given isotope in terms of amu. The isotope is ^{210}_{84} Po, which has a mass of 209.98285u.
I've tried 84(1.007276u) + 126(1.008665u)
thinking that #protons(proton mass in amu) + #neutrons(neutron mass in amu) = mass in amu, give or take.

Can anyone help?

 

[mrjeffy321]

The mass your using, 209.982 amu, is the average atomic mass. This means that, on average, taking all the isotopes and their abundances into account, a sample of Polonium will have a mass of 209.982 g/mol.

But isotopes have whole number masses (you can't have parts of a proton or neutron). The form in which you wrote the isotope gives you the answer,
^{210}_{84} Po
means that the isotope has a mass of 210 gram/mol and an atomic number of 84.

 

[enternaL]

That makes sense. So, how would I get any given isotope's average atomic mass?

 

[mrjeffy321]

elements have an average atomic mass, not isotopes. There maybe several isotopes of a certain element, each isotope having its own, whole-numbered, mass. When you do a weighted average based on the abundance of the isotope, you can get the average atomic mass of the element.
To get the mass of an isotope, just add the protons and neutrons together.

 

[tauceti]

Actually, it is not 210 g/mol.

Its more like 209.98 g/mol. Isotopes doesen't have whole mole mass numbers.

http://www.wolframalpha.com/input/?i=Polonium+210

 

[ehild]

The mass of a nucleus is smaller than the sum of the masses of its free constituents, because of the binding energy.ehild

 

[tauceti]

The mass of a nucleus is smaller than the sum of the masses of its free constituents, because of the binding energy.ehild

But if you sum up the weight of every particle you would get: 126*(1.008664u) + 84*(1.007276u) = 211,702848 u

Greater, not equal to 210.

 

[ehild]

I think you need to convert the mass in amu to kg-s, don't you?


ehild

 

[tauceti]

They are the same, 1 amu = 1 g/mol

 

[ehild]

The unified mass unit is unit for mass and converts to kg in the SI system. 1 amu = 0.001/N_A kg = 1.660538782 * 10^-27 kg.

ehild

 

[I like Serena]

From: http://en.wikipedia.org/wiki/Binding_energy#Mass_excess

It is observed experimentally that the mass of the nucleus is smaller than the number of nucleons each counted with a mass of 1 a.m.u.. This difference is called mass excess.

The difference between the actual mass of the nucleus measured in atomic mass units and the number of nucleons is called mass excess i.e.

Mass excess = M - A = Excess-energy / c2

with : M equals the actual mass of the nucleus, in u.
and : A equals the mass number.

This mass excess is a practical value calculated from experimentally measured nucleon masses and stored in nuclear databases. For middle-weight nuclides this value is negative in contrast to the mass defect which is never negative for any nuclide.

Apparently, to find the exact atomic mass in amu, you have to look it up in a table with experimental results.