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Isotopes and Average Atomic Mass -Solutions
How could a scientist test to separate isotopes of the same element? Isotopes of the same element would
have different masses, so they could be separated by mass.
FILL IN THE TABLE.
Nuclear Symbol
# or Protons
# of Neutrons
Mass #
Sulfur-25
6
6
6
24
24
7
7
16
16
6
7
8
34
39
8
13
7
9
12
13
14
58
63
15
20
23
25
Sodium-12
11
1
12
𝟏𝟑
𝟏𝟏𝑵𝒂
Sodium-13
11
2
13
𝟏𝟏𝟑
𝟓𝟓𝑪𝒔
𝟏𝟏𝟏
𝟓𝟓𝑪𝒔
𝟏𝟎𝟑
𝟓𝟑𝑰
𝟏𝟏𝟏
𝟓𝟑𝑰
𝟑𝟐
𝟏𝟓𝑷
Cesium-113
58
Cesium-111
55
55
Iodine - 103
53
56
50
Iodine - 111
53
58
113
111
103
111
Phosphorus - 111
15
17
32
𝟏𝟐
𝟔𝑪
𝟏𝟑
𝟔𝑪
𝟏𝟒
𝟔𝑪
𝟓𝟖
𝟐𝟒𝑪𝒓
𝟔𝟑
𝟐𝟒𝑪
𝟏𝟓
𝟕𝑵
𝟐𝟎
𝟕𝑵
𝟐𝟑
𝟏𝟔𝑺
𝟐𝟓
𝟏𝟔𝑺
𝟏𝟐
𝟏𝟏𝑵𝒂
Hyphen Notation
Carbon-12
Carbon-13
Carbon-14
Chromium-58
Chromium-63
Nitrogen-15
Nitrogen-20
Sulfur-23
Calculating Average Atomic Mass
1. The natural abundance of Boron isotopes is : 19.9 % B-10 and 80.1% B – 11 Calculate the atomic mass of boron.
Create a table as shown in the example above. Include units with your numbers. (10.80 amu)
Isotope
Mass
% (as decimal)
Subtotal
B-10
10
.199
1.99
B-11
11
.801
8.81
Average Atomic Mass =
10.80
2. The natural abundance of Gallium isotopes is : 60.11 % Ga-69 and 39.89% Ga – 71. Calculate the atomic
mass of Gallium. . Include units with your numbers. (69.8 amu)
Ga - 69
Ga - 71
%
0.6011
0.3989
Mass
69
71
Total ->
Subtotal
41.4759
28.3219
69.7978
HERE ARE SOME MORE
3.
Mass #
24
25
26
%
0.7899
0.1
0.1101
Total ->
18.9576
2.5
2.8626
24.3202
4.
Mass
27.97693
28.9765
29.97377
%
0.9223
0.0467
0.031
Total ->
25.80312
1.353202
0.929187
28.08551
5. HERE IS A MORE CHALLENGING QUESTION REQUIRING SOME ALGEBRA
The atomic mass of Cu is 63.540 amu. It is composed of two isotopes, Cu-63 and Cu-65, with atomic masses of
62.930 and 64.928. What is the % abundance of these isotopes?
Since the total % Abundance = 100% an equation between the two can be written as
X + Y = 100 , assign X = % Abundance of Cu-63 and Y = % Abundance of Cu-65
So Y = 100 – X
63.540 = (63 X) + (65 Y) but this has two unknowns so it cant be solved. Yes, it can if Y = 100 – X is used as
follows:
63.540 = (63 X) + (65(1.00-X)) now solve for X
63.540 = 63X + 65-65X
Now collect the X terms and constants:
Now collect the constants: -1.46 = -2X
63.540 = 65-2X
Divide both sides by -2 which gives the value of X
𝑿=
The other percent 100 – 73 = 27%
−𝟏. 𝟒𝟔
=. 𝟕𝟑
−𝟐
6. In Column D labeled Subtotals Write the Equations (as EXCEL would need them) for calculating the
Average Atomic Mass in the spreadsheet below. Remember that Equations start with_________. No numbers
are needed for an algebraic solution.
7. CONCEPTUAL QUESTION - Silver has an atomic mass of 107.868 amu. Does any atom of any isotope of silver
have a mass of 107.868 amu? Explain why.
No, no isotope of silver will likely have a mass of 107.868 amu. The atomic mass
reported on the Periodic table is an average. This is similar to taking the average
height of students in a classroom. The average represents the group, not any
individual.
Relative Mass of Subatomic Particles
What are the masses of the various items below?
Mass of Electron (kg)
Mass of Neutrons (kg)
-31
9.1 x 10
kg
1.7 x 10
-27
Calculate the mass of the Neutron Relative to the Electron
Mass of Protons(kg)
1.7 x 10-27 kg
kg
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑁𝑒𝑢𝑡𝑟𝑜𝑛
𝑀𝑎𝑠𝑠 𝑜𝑓 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛
=:
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑁𝑒𝑢𝑡𝑟𝑜𝑛 1.7 𝑥10−27 𝑘𝑔
=
= 1.87 × 103
𝑀𝑎𝑠𝑠 𝑜𝑓 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 9.1 𝑥10−31 𝑘𝑔
Calculate the mass of the Proton Relative to the Electron :
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑁𝑒𝑢𝑡𝑟𝑜𝑛 1.7 𝑥10−27 𝑘𝑔
=
= 1.87 × 103
𝑀𝑎𝑠𝑠 𝑜𝑓 𝐸𝑙𝑒𝑐𝑡𝑟𝑜𝑛 9.1 𝑥10−31 𝑘𝑔
The proton and neutron are nearly 2000 times more massive than the electron.
This means the electrons mass is insignificant in the mass of an atom. Below you
will see the % of mass contained in an atom’s electrons is very small.
How do the masses of the proton and neutron compare to one another?
The mass of the proton and neutron are nearly the same.
HOW IS MASS DISTRIBUTED IN AN ATOM? Using Helium-3, you will calculate the % of mass from each type of
particle: protons, neutron and electronsType equation here.
Protons
Neutrons
Electrons
𝟑
𝟑
𝟑
# in 𝟐𝑯𝒆 = 𝟐
# in 𝟐𝑯𝒆 = 𝟏
# in 𝟐𝑯𝒆 = 𝟐
Mass of each proton
Mass of each neutron
Mass of each electron
Mass of protons =
Mass of neutrons =
Mass of electrons =
3.4 x 10
3.4 x 10
18.2 x 10
-27
kg
-27
kg
-31
kg
% of mass which is protons
% of mass which is neutrons
% of mass which is electrons
67 %
33 %
0%
Most of the mass of an atom comes from the protons .
Total Mass (add up the row)
5.1 x 10-27 kg