# Calculating mass of an isotope

1. Nov 29, 2005

### 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?

Last edited: Nov 29, 2005
2. Nov 29, 2005

### mrjeffy321

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

But isotopes have whole number masses (you cant 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.

3. Nov 29, 2005

### enternaL

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

4. Nov 29, 2005

### 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.

5. Apr 10, 2011

### 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

6. Apr 10, 2011

### ehild

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

ehild

7. Apr 10, 2011

### tauceti

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.

8. Apr 10, 2011

### ehild

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

ehild

9. Apr 10, 2011

### tauceti

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

10. Apr 10, 2011

### ehild

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

ehild

11. Apr 11, 2011

### I like Serena

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

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