1. Relative Atomic Mass (RAM)

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Mass Calculations
1. Relative Atomic Mass (RAM)

interconvert mass and amount
need mass of each atom
We are learning to:
a. identify the slight discrepancy between mass number and actual mass
b. explain this in terms of binding energy
c. identify the presence of isotopes as having a far more significant effect upon mass
d. calculate the average mass across all isotopes
...by which time we will have defined Relative Atomic Mass (RAM)

slide 1----------------------------------------------------
 
a. identify the slight discrepancy between mass number and actual mass

slide 2----------------------------------------------------
Would expect there to be a factor of x7 between the masses of these two atoms, but this isn't quite true, because the mass of protons and neutrons varies slightly from one atom to another.
Why does the mass of protons and neutrons vary?
Protons in the nucleus repel each other -- they are all positively charged and like charges repel. To keep them stuck together there must be a force which binds them together. This binding energy causes a reduction in the mass of the nucleus, as some of the mass is turned into energy.
Therefore, generally the larger the atom, the smaller the average mass of the protons and neutrons, because more mass is converted into binding energy.
 
slide 3 -------------------------------------------------

For example, if we compare carbon-12 and hydrogen, and set the carbon value as exactly 12 (and this is what we do; the carbon-12 atom is used as a reference), then we would expect the mass of the hydrogen to be 1, but...due to, in this case, the lack of binding energy, in fact its mass relative to the carbon is 1.007825.
 
slide 4---------------------------
atom mass number mass relative to 12C
1H 1
12C 12
56Fe 56

Summary
o MASS OF PROTONS AND NEUTRONS IS NOT THE SAME IN ALL ATOMS.
o THE ACTUAL MASS OF ATOMS VARIES SLIGHTLY FROM THE MASS NUMBER

slide 4---------------------------
Let's choose another example, to see how this builds up throughout the periodic table. We could do a similar comparison for iron-56 and carbon, and we find that the mass is not 56, but slightly less due to more binding energy, and is in fact 55.934934

1.007825 write as 1.008
12.00000 (by definition) write as 12.000
55.934934 write as 55.934
As you can see, these differences are rather small, and certainly cannot account for this;
 
slide 5-----------------
"Relative atomic mass of copper is 63.55"

Such big deviations from whole numbers are not due to the slight change in mass of the protons and neutrons, they are caused by isotopes; atoms with the same number of protons, but a different number of neturons.
 
slide 6--------------

Isotopes
"Relative atomic mass of copper is 63.55"

Isotope Mass %
63Cu 62.93 69
65Cu 64.93 31

slide 6-------------------
If we put a sample of copper in a mass spectrometer, we get the following result:

We can work out a weighted average across all isotopes:
62.93 x 69% + 64.93 x 31% = 63.55
 
slide 7---------------------------------------------
Isotopes
"Relative atomic mass of copper is 63.55"

Isotope Mass %
63Cu 62.93 69
65Cu 64.93 31

62.93 x 69% + 64.93 x 31% = 63.55
Summary
o WEIGHTED AVERAGE ACROSS ALL ISOTOPES

slide 7---------------------------------------------
summary: the weighted average across all isotopes gives us a useful value for the mass of copper atoms. If we have an amount of copper, it will include both isotopes and we must account for this when interconverting mass and numbers of atoms.
 
slide 8-----------------------
RELATIVE ATOMIC MASS

to 12C averaged across all isotopes
 
Assessment

1. Cobalt exists only as the 59Co isotope. What would you expect the relative atomic mass of cobalt to be?
A. slightly higher than 59
due to more binding energy than 12C B. slightly lower than 59
due to more binding energy than 12C
C. slightly lower than 59
due to less binding energy than 12C D. slightly higher than 59
due to less binding energy than 12C

2. If approximately 20% of boron is the 10B isotope and 80% is the 11B isotope, estimate the relative atomic mass of boron
A. (0.2 x 10) + (0.8 x 11) = 10.2 B. (0.2 x 11) + (0.8 x 10) = 10.2
C. (0.2 x 10) + (0.8 x 11) = 10.8 D. (0.2 x 11) + (0.8 x 10) = 10.8

Answers 1. B, 2. C