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Mass Defect

Key Concepts

  • Atoms are made up of protons, neutrons and electrons.

  • Each proton, neutron and electron has a rest mass.

  • Mass defect is the difference in mass between the observed (measured) mass of an atom and the mass calculated using the mass of all the protons, neutrons and electrons present.

    Δm = (Z × mp) + (Z × me) + ([A-Z] × mn) - M
    where:
        Δm = mass defect
        Z = atomic number (number of protons)
        A = mass number (number of protons and neutrons)
        mp = rest mass of a proton
        mn = rest mass of a neutron
        me = rest mass of an electron
        M = observed atomic mass of the atom

  • Mass defect is often calculated in units of "atomic mass units" (u)1 or the SI units2 of kilograms (kg)

  • 1 u = 1.661 × 10-27 kg

Observed (measured) Mass of Atoms

Mass spectroscopy is used to determine the mass of the isotopes of an element3.

The observed mass, the mass observed using mass spectroscopy, of some isotopes is given in the table on the right in "atomic mass units" and in the SI units of kilograms (kg).

Predicting the Mass of an Atom of an Isotope of an Element

An atom is made up of a number of electrons surrounding a nucleus containing a number of protons and neutrons.

The protons and neutrons in a nucleus are referred to as nucleons.

An isotope of an element with the chemical symbol E and a mass number A and an atomic number Z can be written in one of three ways:

element-A or A E or AE
Z  

where:

  Z = atomic number (given in Periodic Table)
    = number of protons in the nucleus of the atom

  A = mass number (given in isotope's name or symbol)
    = number of protons plus number of neutrons

Therefore we can calculate the number of neutrons in the nucleus of the atom:

No. neutrons = mass number - atomic number
No. neutrons = A - Z

The number of negatively charged electrons surrounding the nucleus of a neutral atom, that is an atom with no overall charge, equals the number of positively charged protons in the nucleus, so:

No. electrons in neutral atom
    = No. protons in nucleus
    = atomic number
    = Z

Each of these subatomic particles (protons, neutrons and electrons) has a rest mass.

The rest mass of protons, neutrons and electrons is usually given to you on a data sheet.
These masses given below are in "atomic mass units" and in the SI units of mass, kilograms (kg):

Subatomic
Particle
Rest Mass
atomic mass units
Rest Mass
kg
proton 1.007276 1.673 x 10-27
neutron 1.008665 1.675 x 10-27
electron 0.000549 9.109 x 10-31

We can use the information provided in the symbol for the isotope along with the information supplied in the table above to calculate the predicted mass of an isotope of the element:

predicted
mass of atom
= mass of
all protons
+ mass of
all neutrons
+ mass of
all electrons
  = (Z × mass proton) + ([A − Z] × mass neutron) + (Z × mass electron)

For example, we can calculate the predicted mass of an atom of hydrogen-1, 1H, in kilograms:

Symbol for this hydrogen isotope is 1 H
1

No. protons = atomic number (Z)
No. protons = 1
    (from Periodic Table)

No. neutrons = mass number (A) - atomic number (Z)
No. neutrons = 1 - 1 = 0
    (mass number given in the question, 1H)

No. electrons in the neutral atom = atomic number (Z)
No. electrons = 1

mass of a proton = mp = 1.673 × 10-27 kg

mass of a neutron = mn = 1.675 × 10-27 kg

mass of an electron = me = 9.109 × 10-31 kg

predicted mass 1H atom in kg
= (Z × mp) + ([A − Z] × mn) + (Z × me)
= (1 × 1.673 x 10-27) + ([1 − 1] × 1.675 x 10-27) + (1 × 9.109 x 10-31)
= 1.673 x 10-27 + 0 + 9.109 x 10-31
= 1.674 x 10-27 kg        

Similarly we can predict the mass of an atom of deuterium, the hydrogen-2 or 2H isotope, in kilograms:

Symbol for this hydrogen isotope is 2 H
1

No. protons = atomic number (Z)
No. protons = 1
    (from Periodic Table)

No. neutrons = mass number (A) - atomic number (Z)
No. neutrons = 2 - 1 = 1
    (mass number given in the question, 2H)

No. electrons in the neutral atom = atomic number (Z)
No. electrons = 1

mass of a proton = mp = 1.673 × 10-27 kg

mass of a neutron = mn = 1.675 × 10-27 kg

mass of an electron = me = 9.109 × 10-31 kg

predicted mass of 2H atom in kg
= (Z × mp) + ([A − Z] × mn) + (Z × me)
= (1 × 1.673 x 10-27) + ([2 − 1] × 1.675 x 10-27) + (1 × 9.109 x 10-31)
= 1.673 x 10-27 + 1.675 x 10-27 + 9.109 x 10-31
= 3.349 x 10-27 kg        

We can also predict the mass of an atom of an isotope of an element in "atomic mass units" if required.

For example, we can predict the mass of the deuterium, hydrogen-2 or 2H, atom in "atomic mass units":

No. protons = atomic number (Z)
No. protons = 1
    (from Periodic Table)

No. neutrons = mass number (A) - atomic number (Z)
No. neutrons = 2 - 1 = 1
    (mass number given in the question, 2H)

No. electrons in the neutral atom = atomic number (Z)
No. electrons = 1

mass of a proton = mp = 1.007276 u

mass of a neutron = mn = 1.008665 u

mass of an electron = me = 0.000549 u

predicted mass of 2H atom in atomic mass units
= (Z × mp) + ([A − Z] × mn) + (Z × me)
= (1 × 1.007276) + ([2 − 1] × 1.008665) + (1 × 0.000549)
= 1.007276 + 1.008665 + 0.000549
= 2.01649 u        

Mass Conversions: kilograms and atomic mass units

The SI unit of mass is the kilogram, kg, which is an incredibly huge unit to use when talking about the mass of an atom. As we discovered above, the mass of an atom of hydrogen-1 is found to be 1.674 × 10-27 kg.
Physicists often prefer to work in "atomic mass units", u, rather than kilograms, kg.
Since the mass of an atom is its mass relative to an atom of the carbon-12 atom, and the mass of the carbon-12 atom is defined as 12.000 000 atomic mass units (12.000 000 u),
then 1 atomic mass unit = 1/12 the mass of the carbon-12 atom.
The mass of the carbon-12 atom has been determined to be 1.993 × 10-26 kg
1 atomic mass unit = 1/12 × 1.993 × 10-26 = 1.661 × 10-27 kg

So if the mass of the hydrogen-1 atom has been given in atomic mass units as 1.007 u, we can convert this to a mass in kilograms by multiplying by 1.661 × 10-27:

mass 1H = 1.007 u

mass 1H = 1.007 u × 1.661 × 10-27 kg/u
            = 1.673 kg

If the mass of the hydrogen-2 atom has been given as 3.344 × 10-27 kg we can convert this to atomic mass units by dividing by 1.661 × 10-27:

mass 2H = 3.344 × 10-27 kg

mass 2H = 3.344 × 10-27 kg ÷ 1.661 × 10-27 kg/u
            = 2.013 u

Mass Defect

Compare the values for the predicted mass of the atom of each isotope of hydrogen we calculated in the first section, with its observed (measured) value from the table on the right:

hydrogen
isotope
predicted
mass / kg
observed
mass /kg
1H 1.674 × 10-27 1.674 × 10-27
2H 3.349 × 10-27 3.344 × 10-27

For the hydrogen-1 isotope, 1H, the predicted mass and the observed mass are the same.

However, the mass we predicted for an atom of the deuterium isotope, 2H, is greater than the mass observed when scientists measure the mass of the deuterium atom.

In fact, with the exception of 1H, the predicted mass of an atom based on calculations of the total mass of protons, neutrons and electrons it contains is always greater than the mass of the atom when it is measured!

This difference between predicted and observed mass of an atom is called the mass defect.

Mass defect is usually given the symbol Δm (to represent an observable change in mass), and the mass of an atom is usually given the symbol M (or Mr for relative atomic mass).

mass defect = predicted mass - observed mass

Δm = (Z × mass of proton) + ([A-Z] × mass of neutron) + (Z × mass of electron) - M
Δm = (Z × mp) + ([A-Z] × mn) + (Z × me) - M

We can calculate the mass defect for an atom of the 2H isotope in kilograms as:

observed mass = 3.344 × 10-27 kg (from table)
predicted mass = 3.349 × 10-27 kg (calculated above)

mass defect = predicted mass - observed mass
Δm = 3.349 × 10-27 - 3.344 × 10-27
  = 5 × 10-30 kg    

Similarly we can calculate the mass defect for the 2H atom in "atomic mass units" (u):

observed mass = 2.014 u (from table)
predicted mass = 2.016 u (calculated above)

mass defect = predicted mass - observed mass
Δm = 2.016 - 2.014
  = 0.002 u    

The mass defect can be used to calculate the nuclear binding energy and hence explain the stability of certain isotopes.

Worked Examples
(based on StoPGoPS method of problem solving)

Worked Example 1.

Question:
The mass of an atom of uranium-235 is observed to be 235.044 u.
Calculate the mass defect for this atom in atomic mass units given the following data:

  • mass of a proton = 1.007276 u

  • mass of a neutron = 1.008665 u

  • mass of an electron = 0.000549 u

Solution:

  1. What is the question asking you to do?

    Calculate the mass defect in atomic mass units.

  2. (i) What data have you been given?

    isotope: uranium-235
    observed mass of an atom of 235U = 235.044 u
    proton mass = 1.007276 u
    neutron mass = 1.008665 u
    electron mass = 0.000549 u

    (ii) What is the relationship between what you know and what you need to find?

    mass defect = predicted mass - observed mass

    predicted mass = (Z × proton mass) + ([A-Z] × neutron mass) + (Z × electron mass)

  3. Calculate the mass defect

    For 235U:

    Z = 92 (from Periodic Table)
    A = 235 (from data in question)

    Predicted mass of 235U
    predicted mass = (Z × proton mass) + ([A-Z] × neutron mass) + (Z × electron mass)
    predicted mass = (92 × 1.007276) + (143 × 1.008665) + (92 × 0.000549)
    predicted mass = 92.6694 + 144.2391 + 0.0505
    predicted mass = 236.959 u

    Calculate mass defect
    mass defect = predicted mass - observed mass
    mass defect = 236.959 - 235.044
    mass defect = 1.915 u

  4. Is your answer plausible?
    Observed mass of an atom is always less than the predicted mass.
    The mass we predicted is greater than the observed mass so this answer is plausible.

  5. State the solution to the problem
    Mass defect for uranium-235 is 1.915 atomic mass units.

Worked Example 2.

Question:
The mass of an atom of uranium-238 is observed to be 3.953 × 10-25 kg.
Calculate the mass defect for this atom in kilograms.

Solution

  1. What is the question asking you to do?

    Calculate the mass defect in kilograms.

  2. (i) What data have you been given?

    isotope: uranium-238
    observed mass of an atom of 238U = 3.953 × 10-25 kg

    (ii) What is the relationship between what you know and what you need to find?

    mass defect = predicted mass - observed mass

    predicted mass = (Z × proton mass) + ([A-Z] × neutron mass) + (Z × electron mass)

  3. Calculate the mass defect

    For 238U:

    Z = 92 (from Periodic Table)
    A = 238 (from data in question)

    From the data sheet

    proton mass = 1.673 × 10-27 kg
    neutron mass = 1.675 × 10-27 kg
    electron mass = 9.109 × 10-31 kg

    Predict mass of 238U
    predicted mass = (Z × proton mass) + ([A-Z] × neutron mass) + (Z × electron mass)
    predicted mass = (92 × 1.673 × 10-27) + (146 × 1.675 × 10-27) + (92 × 9.109 × 10-31)
    predicted mass = 1.539 × 10-25 + 2.446 × 10-25 + 8.380 × 10-29
    predicted mass = 3.983 × 10-25 kg

    Calculate mass defect
    mass defect = predicted mass - observed mass
    mass defect = 3.983 × 10-25 - 3.953 × 10-25
    mass defect = 3.000 × 10-27 kg

  4. Is your answer plausible?
    Observed mass of an atom is always less than the predicted mass.
    The mass we predicted is greater than the observed mass so this answer is plausible.

  5. State the solution to the problem
    Mass defect for uranium-238 is 3.983 × 10-25 kg.

Drill

Quick Questions: 1

Calculate the mass defect for magnesium-25 given
mass of proton = 1.007276 u
mass of neutron = 1.008665 u
mass of electron = 0.000549 u
observed mass magnesium-25 = 24.986

Δm = u     Check


1Chemists often don't use units when referring to the atomic mass (atomic weight) of an element because it is a weighted average relative to the mass of carbon-12, however, Physicists (and some Chemists) prefer to define an atomic mass unit (u) and use this as the unit of measurement for atomic mass (atomic weight).

2SI is the abbreviation for Système International d'Unités. The General Conference of Weights and Measures agreed on a unified version of the metric system in 1960. The units of measurement in this system are known as SI units.

3Chemistry students in an introductory course usually use isotopic masses that have been "rounded off" to calculate the relative atomic weight (relative atomic mass) of an element. In this way it is possible to use the mass number of an isotope as its atomic weight.

Once you have been introduced to Mass Spectroscopy you can then use the observed isotopic masses to calculate the relative atomic weight (atomic mass) of an element.


What would you like to do now?
Element
Name
Atomic
Number
Isotope
Symbol
Mass
atomic mass units
Mass
kg
hydrogen 1 1H 1.007 1.674 × 10-27
2H 2.014 3.344 × 10-27
3H 3.016 5.008 × 10-27
helium 2 3He 3.016 5.008 × 10-27
4He 4.003 6.646 × 10-27
lithium 3 6Li 6.015 9.988 × 10-27
7Li 7.016 1.165 × 10-26
beryllium 4 9Be 9.012 1.497 × 10-26
boron 5 10B 10.013 1.663 × 10-26
11B 11.009 1.828 × 10-26
carbon 6 12C 12.000 1.993 × 10-26
13C 13.003 2.159 × 10-26
14C 14.003 2.325 × 10-26
nitrogen 7 14N 14.003 2.325 × 10-26
15N 15.000 2.491 × 10-26
oxygen 8 16O 15.995 2.656 × 10-26
17O 16.999 2.823 × 10-26
18O 17.999 2.989 × 10-26
fluorine 9 19F 18.998 3.155 × 10-26
neon 10 20Ne 19.992 3.320 × 10-26
21Ne 20.994 3.486 × 10-26
22Ne 21.991 3.652 × 10-26
sodium 11 23Na 22.990 3.818 × 10-26
magnesium 12 24Mg 23.985 3.983 × 10-26
25Mg 24.986 4.149 × 10-26
26Mg 25.983 4.315 × 10-26
aluminium 13 27Al 26.982 4.480 × 10-26
silicon 14 28Si 27.977 4.646 × 10-26
29Si 28.976 4.812 × 10-26
30Si 29.974 4.977 × 10-26
phosphorus 15 31P 30.974 5.143 × 10-26
sulfur 16 32S 31.972 5.309 × 10-26
33S 32.971 5.475 × 10-26
34S 33.968 5.641 × 10-26
36S 35.967 5.973 × 10-26
chlorine 17 35Cl 34.969 5.807 × 10-26
37Cl 36.966 6.138 × 10-26
argon 18 36Ar 35.968 5.973 × 10-26
38Ar 37.963 6.304 × 10-26
40Ar 39.962 6.636 × 10-26
potassium 19 39K 38.964 6.470 × 10-26
40K 39.964 6.636 × 10-26
41K 40.962 6.802 × 10-26
calcium 20 40Ca 39.963 6.636 × 10-26
42Ca 41.959 6.968 × 10-26
43Ca 42.959 7.134 × 10-26
44Ca 43.955 7.299 × 10-26
46Ca 45.954 7.631 × 10-26
48Ca 47.953 7.963 × 10-26
scandium 21 45Sc 44.956 7.465 × 10-26
titanium 22 46Ti 45.953 7.631 × 10-26
47Ti 46.952 7.797 × 10-26
48Ti 47.948 7.962 × 10-26
49Ti 48.948 8.128 × 10-26
50Ti 49.945 8.294 × 10-26
vanadium 23 50V 49.947 8.294 × 10-26
51V 50.944 8.460 × 10-26
chromium 24 50Cr 49.946 8.294 × 10-26
52Cr 51.941 8.625 × 10-26
53Cr 52.941 8.791 × 10-26
54Cr 53.939 8.957 × 10-26
manganese 25 55Mn 54.938 9.123 × 10-26
iron 26 54Fe 53.940 8.957 × 10-26
56Fe 55.935 9.288 × 10-26
57Fe 56.935 9.455 × 10-26
58Fe 57.933 9.620 × 10-26
cobalt 27 59Co 58.933 9.786 × 10-26
nickel 28 58Ni 57.935 9.621 × 10-26
60Ni 59.931 9.952 × 10-26
61Ni 60.931 1.012 × 10-25
62Ni 61.928 1.028 × 10-25
64Ni 63.928 1.062 × 10-25
copper 29 63Cu 62.930 1.045 × 10-25
65Cu 64.928 1.078 × 10-25
zinc 30 64Zn 63.929 1.062 × 10-25
66Zn 65.926 1.095 × 10-25
67Zn 66.927 1.111 × 10-25
68Zn 67.925 1.128 × 10-25
70Zn 69.925 1.161 × 10-25
gallium 31 69Ga 68.926 1.145 × 10-25
71Ga 70.925 1.178 × 10-25
germanium 32 70Ge 69.924 1.161 × 10-25
72Ge 71.922 1.194 × 10-25
73Ge 72.923 1.211 × 10-25
74Ge 73.921 1.228 × 10-25
76Ge 75.921 1.261 × 10-25
arsenic 33 75As 74.922 1.244 × 10-25
selenium 34 74Se 73.922 1.228 × 10-25
76Se 75.919 1.261 × 10-25
77Se 76.920 1.277 × 10-25
78Se 77.917 1.294 × 10-25
80Se 79.917 1.327 × 10-25
82Se 81.917 1.360 × 10-25
bromine 35 79Br 78.918 1.310 × 10-25
81Br 80.916 1.344 × 10-25
krypton 36 78Kr 77.920 1.294 × 10-25
80Kr 79.916 1.327 × 10-25
82Kr 81.913 1.360 × 10-25
83Kr 82.914 1.377 × 10-25
84Kr 83.912 1.393 × 10-25
86Kr 85.911 1.427 × 10-25
rubidium 37 85Rb 84.912 1.410 × 10-25
87Rb 86.909 1.44 × 10-25
strontium 38 84Sr 83.913 1.393 × 10-25
86Sr 85.909 1.427 × 10-25
87Sr 86.909 1.443 × 10-25
88Sr 87.906 1.460 × 10-25
yttrium 39 89Y 88.906 1.476 × 10-25
zirconium 40 90Zr 89.905 1.493 × 10-25
91Zr 90.907 1.510 × 10-25
92Zr 91.905 1.526 × 10-25
94Zr 93.906 1.559 × 10-25
96Zr 95.908 1.593 × 10-25
niobium 41 93Nb 92.906 1.543 × 10-25
molybdenum 42 92Mo 91.907 1.526 × 10-25
94Mo 93.905 1.559 × 10-25
95Mo 94.906 1.576 × 10-25
96Mo 95.905 1.593 × 10-25
97Mo 96.906 1.609 × 10-25
98Mo 97.905 1.623 × 10-25
100Mo 99.907 1.659 × 10-25
technetium 43 97Tc 96.906 1.609 × 10-25
98Tc 97.907 1.626 × 10-25
99Tc 98.906 1.642 × 10-25
ruthenium 44 96Ru 95.908 1.593 × 10-25
98Ru 97.905 1.623 × 10-25
99Ru 98.906 1.642 × 10-25
100Ru 99.904 1.659 × 10-25
101Ru 100.906 1.676 × 10-25
102Ru 101.904 1.692 × 10-25
104Ru 103.905 1.725 × 10-25
rhodium 45 103Rh 102.906 1.709 × 10-25
palladium 46 102Pd 101.906 1.692 × 10-25
104Pd 103.904 1.725 × 10-25
105Pd 104.905 1.742 × 10-25
106Pd 105.903 1.759 × 10-25
108Pd 107.903 1.792 × 10-25
110Pd 109.905 1.825 × 10-25
silver 47 107Ag 106.905 1.775 × 10-25
109Ag 108.905 1.808 × 10-25
cadmium 48 106Cd 105.906 1.759 × 10-25
108Cd 107.904 1.792 × 10-25
110Cd 109.903 1.825 × 10-25
111Cd 110.904 1.842 × 10-25
112 111.903 1.858 × 10-25
113Cd 112.904 1.875 × 10-25
114Cd 113.903 1.891 × 10-25
116Cd 115.905 1.925 × 10-25
indium 49 113In 112.904 1.875 × 10-25
115In 114.904 1.908 × 10-25
tin 50 112Sn 111.905 1.858 × 10-25
114Sn 113.903 1.891 × 10-25
115Sn 114.903 1.908 × 10-25
116Sn 115.902 1.925 × 10-25
117Sn 116.903 1.941 × 10-25
118Sn 117.902 1.958 × 10-25
119Sn 118.903 1.974 × 10-25
120Sn 119.902 1.991 × 10-25
122Sn 121.903 2.024 × 10-25
124Sn 123.905 2.058 × 10-25
antimony 51 121Sb 120.904 2.008 × 10-25
123Sb 122.904 2.041 × 10-25
tellurium 52 120Te 119.904 1.991 × 10-25
122Te 121.903 2.024 × 10-25
123Te 122.904 2.041 × 10-25
124Te 123.903 2.058 × 10-25
125Te 124.904 2.074 × 10-25
126Te 125.903 2.091 × 10-25
128Te 127.904 2.124 × 10-25
130Te 129.906 2.157 × 10-25
iodine 53 127I 126.904 2.107 × 10-25
xenon 54 124Xe 123.906 2.058 × 10-25
126Xe 125.904 2.091 × 10-25
128Xe 127.906 2.124 × 10-25
129Xe 128.905 2.141 × 10-25
130Xe 129.904 2.157 × 10-25
131Xe 130.905 2.174 × 10-25
132Xe 131.904 2.190 × 10-25
134Xe 133.905 2.224 × 10-25
136Xe 135.907 2.257 × 10-25
cesium 55 133Cs 132.905 2.207 × 10-25
barium 56 130Ba 129.906 2.157 × 10-25
132Ba 131.905 2.190 × 10-25
134Ba 133.905 2.224 × 10-25
135Ba 134.906 2.240 × 10-25
136Ba 135.905 2.257 × 10-25
137Ba 136.906 2.273 × 10-25
138Ba 137.905 2.290 × 10-25
lanthanum 57 138La 137.907 2.290 × 10-25
139La 138.906 2.307 × 10-25
cerium 58 136Ce 135.907 2.257 × 10-25
138Ce 137.906 2.290 × 10-25
140Ce 139.905 2.323 × 10-25
142Ce 141.909 2.357 × 10-25
praseodymium 59 141Pr 140.908 2.340 × 10-25
neodymium 60 142Nd 141.908 2.356 × 10-25
143Nd 142.910 2.373 × 10-25
144Nd 143.910 2.390 × 10-25
145Nd 144.913 2.406 × 10-25
146Nd 145.913 2.423 × 10-25
148Nd 147.917 2.456 × 10-25
150Nd 149.921 2.490 × 10-25
promethium 61 145Pm 144.913 2.406 × 10-25
147Pm 146.915 2.440 × 10-25
samarium 62 144Sm 143.912 2.390 × 10-25
147Sm 146.915 2.440 × 10-25
148Sm 147.915 2.456 × 10-25
149Sm 148.917 2.473 × 10-25
150Sm 149.917 2.489 × 10-25
152Sm 151.920 2.523 × 10-25
154Sm 153.922 2.556 × 10-25
europium 63 151Eu 150.920 2.506 × 10-25
153Eu 152.921 2.539 × 10-25
gadolinium 64 152Gd 151.920 2.523 × 10-25
154Gd 153.921 2.556 × 10-25
155Gd 154.923 2.573 × 10-25
156Gd 155.922 2.589 × 10-25
157Gd 156.924 2.606 × 10-25
158Gd 157.924 2.622 × 10-25
160Gd 159.927 2.656 × 10-25
terbium 65 159Tb 158.925 2.639 × 10-25
dysprosium 66 156Dy 155.924 2.589 × 10-25
158Dy 157.924 2.622 × 10-25
160Dy 159.925 2.656 × 10-25
161Dy 160.927 2.672 × 10-25
162Dy 161.927 2.689 × 10-25
163Dy 162.929 2.706 × 10-25
164Dy 163.929 2.722 × 10-25
holmium 67 165Ho 164.930 2.739 × 10-25
erbium 68 162Er 161.929 2.698 × 10-25
164Er 163.929 2.722 × 10-25
166Er 165.930 2.755 × 10-25
167Er 166.932 2.772 × 10-25
168Er 167.932 2.789 × 10-25
170Er 169.935 2.822 × 10-25
thulium 69 169Tm 168.934 2.805 × 10-25
ytterbium 70 168Yb 167.934 2.789 × 10-25
170Yb 169.935 2.822 × 10-25
171Yb 170.936 2.839 × 10-25
172Yb 171.936 2.855 × 10-25
173Yb 172.938 2.872 × 10-25
174Yb 173.939 2.888 × 10-25
176Yb 175.943 2.922 × 10-25
lutetium 71 175Lu 174.941 2.905 × 10-25
176Lu 175.943 2.922 × 10-25
hafnium 72 174Hf 173.940 2.888 × 10-25
176Hf 175.941 2.922 × 10-25
177Hf 176.943 2.938 × 10-25
178Hf 177.944 2.955 × 10-25
179Hf 178.946 2.972 × 10-25
180Hf 179.947 2.980 × 10-25
tantalum 73 180Ta 179.947 2.988 × 10-25
181Ta 180.948 3.00 × 10-25
tungsten 74 180W 179.947 2.988 × 10-25
182W 181.948 3.021 × 10-25
183W 182.950 3.038 × 10-25
184W 183.951 3.055 × 10-25
186W 185.954 3.088 × 10-25
rhenium 75 185Re 184.953 3.071 × 10-25
187Re 186.956 3.105 × 10-25
osmium 76 184Os 183.952 3.055 × 10-25
186Os 185.954 3.088 × 10-25
187Os 186.956 3.105 × 10-25
188Os 187.956 3.121 × 10-25
189Os 188.958 3.138 × 10-25
190Os 189.958 3.148 × 10-25
192Os 191.961 3.188 × 10-25
iridium 77 191Ir 190.961 3.171 × 10-25
193Ir 192.963 3.204 × 10-25
platinum 78 190Pt 189.960 3.154 × 10-25
192Pt 191.961 3.188 × 10-25
194Pt 193.963 3.221 × 10-25
195Pt 194.965 3.238 × 10-25
196Pt 195.965 3.254 × 10-25
198Pt 197.968 3.287 × 10-25
gold 79 197Au 196.667 3.266 × 10-25
mercury 80 196Hg 195.966 3.254 × 10-25
198Hg 197.967 3.288 × 10-25
199Hg 198.968 3.304 × 10-25
200Hg 199.968 3.321 × 10-25
201Hg 200.970 3.337 × 10-25
202Hg 201.971 3.354 × 10-25
204Hg 203.973 3.387 × 10-25
thallium 81 203Tl 202.972 3.371 × 10-25
205Tl 204.974 3.404 × 10-25
lead 82 204Pb 203.973 3.387 × 10-25
206Pb 205.974 3.420 × 10-25
207Pb 206.976 3.437 × 10-25
208Pb 207.977 3.454 × 10-25
bismuth 83 209Bi 208.980 3.470 × 10-25
polonium 84 209Po 208.982 3.470 × 10-25
210Po 209.983 3.487 × 10-25
astatine 85 210At 209.987 3.487 × 10-25
211At 210.987 3.504 × 10-25
radon 86 211Rn 210.991 3.504 × 10-25
220Rn 220.011 3.653 × 10-25
222Rn 222.018 3.687 × 10-25
francium 87 223Fr 223.020 3.703 × 10-25
radium 88 223Ra 223.019 3.703 × 10-25
224Ra 224.020 3.720 × 10-25
226Ra 226.025 3.753 × 10-25
228Ra 228.031 3.787 × 10-25
actinium 89 227Ac 227.028 3.770 × 10-25
thorium 90 230Th 230.033 3.820 × 10-25
232Th 232.038 3.853 × 10-25
protactinuim 91 231Pa 231.036 3.837 × 10-25
uranium 92 233U 233.040 3.870 × 10-25
234U 234.041 3.886 × 10-25
235U 235.044 3.903 × 10-25
236U 236.045 3.920 × 10-25
238U 238.051 3.953 × 10-25
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