[www.flickr.com] You have a pile of rocks to move and need to decide what equipment you want to rent to move them. If the rocks are fairly small, you can get a shovel to pick them up. Larger rocks could be moved by hand, but big boulders will need some sort of mechanical scoop. The amount of each kind of rock will also determine how much time you will need to get the job done. Knowing the relative amounts of large, medium, and small rocks can be very useful in deciding how to approach the job.
Most elements occur naturally as a mixture of two or more isotopes. The table below shows the natural isotopes of several elements, along with the percent natural abundance of each.
Hydrogen | \(\ce{_1^1H}\) | 99.985 | 1.0078 | 1.0080 |
\(\ce{_1^2H}\) | 0.015 | 2.0141 | ||
\(\ce{_1^3H}\) | negligible | 3.0160 | ||
Carbon | \(\ce{_6^{12}C}\) | 98.89 | 12.000 | 12.011 |
\(\ce{_6^{13}C}\) | 1.11 | 13.003 | ||
\(\ce{_6^{14}C}\) | trace | 14.003 | ||
Oxygen | \(\ce{_8^{16}O}\) | 99.759 | 15.995 | 15.999 |
\(\ce{_8^{17}O}\) | 0.037 | 16.995 | ||
\(\ce{_8^{18}O}\) | 0.204 | 17.999 | ||
Chlorine | \(\ce{_{17}^{35}Cl}\) | 75.77 | 34.969 | 35.453 |
\(\ce{_{17}^{37}Cl}\) | 24.23 | 36.966 | ||
Copper | \(\ce{_{29}^{63}Cu}\) | 69.17 | 62.930 | 63.546 |
\(\ce{_{29}^{65}Cu}\) | 30.83 | 64.928 |
For some elements, one particular isotope predominates greatly over the other isotopes. Naturally occurring hydrogen is nearly all hydrogen-1 and naturally occurring oxygen is nearly all oxygen-16. For many other elements, however, more than one isotope may exist in more substantial quantities. Chlorine (atomic number 17) is a yellowish-green toxic gas. About three quarters of all chlorine atoms have 18 neutrons, giving those atoms a mass number of 35. About one quarter of all chlorine atoms have 20 neutrons, giving those atoms a mass number of 37. Were you to simply calculate the arithmetic average of the precise atomic masses, you would get 36.
\[\frac{\left( 34.969 + 36.966 \right)}{2} = 35.968 \: \text{amu}\nonumber \]
Clearly the actual average atomic mass from the last column of the table is significantly lower. Why? We need to take into account the percent natural abundance of each isotope, in order to calculate the weighted average. The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element. The sample problem below demonstrates how to calculate the atomic mass of chlorine.
Use the atomic masses of each of the two isotopes of chlorine along with their respective percent abundances to calculate the average atomic mass of chlorine.
Solution Step 1: List the known and unknown quantities and plan the problem. Known- Chlorine-35: atomic mass \(= 34.969 \: \text{amu}\) and percent abundance \(= 75.77\%\)
- Chlorine-37: atomic mass \(= 36.966 \: \text{amu}\) and percent abundance \(= 24.23\%\)
- Average atomic mass of chlorine
Change each percent abundance into decimal form by dividing by 100. Multiply this value by the atomic mass of that isotope. Add together for each isotope to get the average atomic mass.
\[\begin{array}{ll} \text{chlorine-35} & 0.7577 \times 34.969 = 26.50 \: \text{amu} \\ \text{chlorine-37} & 0.2423 \times 36.966 = 8.957 \: \text{amu} \\ \text{average atomic mass} & 26.50 + 8.957 = 35.46 \: \text{amu} \end{array}\nonumber \]
Note: Applying significant figure rules results in the \(35.45 \: \text{amu}\) result without excessive rounding error. In one step:
\[\left( 0.7577 \times 34.969 \right) + \left(0.2423 \times 36.966 \right) = 35.46 \: \text{amu}\nonumber \]
The calculated average atomic mass is closer to 35 than to 37 because a greater percentage of naturally occurring chlorine atoms have the mass number of 35. It agrees with the value from the table above.
Summary
- The atomic mass of an element is the weighted average of the atomic masses of the naturally occurring isotopes of that element.
- Calculations of atomic mass use the percent abundance of each isotope.
- Define atomic mass.
- What information do you need to calculate atomic mass for an element?
- Calculate the atomic mass for carbon using the data provided in the table below.
carbon-12 | 12.000000 | 98.90 |
carbon-13 | 13.003355 | 1.100 |
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This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Chlorine (17Cl) has 25 isotopes with mass numbers ranging from 28Cl to 52Cl and 2 isomers (34mCl and 38mCl). There are two stable isotopes, 35Cl (75.77%) and 37Cl (24.23%), giving chlorine a standard atomic weight of 35.45. The longest-lived radioactive isotope is 36Cl, which has a half-life of 301,000 years. All other isotopes have half-lives under 1 hour, many less than one second. The shortest-lived are 29Cl and 30Cl, with half-lives less than 10 picoseconds and 30 nanoseconds, respectively—the half-life of 28Cl is unknown.
Find sources: "Isotopes of chlorine" – news · newspapers · books · scholar · JSTOR (May 2018) (Learn how and when to remove this template message)
Standard atomic weight Ar°(Cl)Isotope
Decay
abundance
half-life (t1/2)
mode
product
35Cl
76%
stable
36Cl
trace
3.01×105 y
β−
36Ar
ε
36S
37Cl
24%
stable
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28Cl[5] | 17 | 11 | 28.02954(64)# | p | 27S | 1+# | |||
29Cl[5] | 17 | 12 | 29.01413(20) | <10 ps | p | 28S | (1/2+) | ||
30Cl[5] | 17 | 13 | 30.00477(21)# | <30 ns | p | 29S | 3+# | ||
31Cl | 17 | 14 | 30.992448(4) | 190(1) ms | β+ (97.6%) | 31S | 3/2+ | ||
β+, p (2.4%) | 30P | ||||||||
32Cl | 17 | 15 | 31.9856846(6) | 298(1) ms | β+ (99.92%) | 32S | 1+ | ||
β+, α (.054%) | 28Si | ||||||||
β+, p (.026%) | 31P | ||||||||
33Cl | 17 | 16 | 32.9774520(4) | 2.5038(22) s | β+ | 33S | 3/2+ | ||
34Cl | 17 | 17 | 33.97376249(5) | 1.5266(4) s | β+ | 34S | 0+ | ||
34mCl | 146.360(27) keV | 31.99(3) min | β+ (55.4%) | 34S | 3+ | ||||
IT (44.6%) | 34Cl | ||||||||
35Cl | 17 | 18 | 34.96885269(4) | Stable | 3/2+ | 0.7576(10) | 0.75644–0.75923 | ||
36Cl[n 8] | 17 | 19 | 35.96830682(4) | 3.013(15)×105 y | β− (98.1%) | 36Ar | 2+ | Trace[n 9] | approx. 7×10−13 |
β+ (1.9%) | 36S | ||||||||
37Cl | 17 | 20 | 36.96590258(6) | Stable | 3/2+ | 0.2424(10) | 0.24077–0.24356 | ||
38Cl | 17 | 21 | 37.96801042(11) | 37.24(5) min | β− | 38Ar | 2− | ||
38mCl | 671.365(8) keV | 715(3) ms | IT | 38Cl | 5− | ||||
39Cl | 17 | 22 | 38.9680082(19) | 56.2(6) min | β− | 39Ar | 3/2+ | ||
40Cl | 17 | 23 | 39.97042(3) | 1.35(2) min | β− | 40Ar | 2− | ||
41Cl | 17 | 24 | 40.97068(7) | 38.4(8) s | β− | 41Ar | (1/2+,3/2+) | ||
42Cl | 17 | 25 | 41.97334(6) | 6.8(3) s | β− | 42Ar | |||
43Cl | 17 | 26 | 42.97406(7) | 3.13(9) s | β− (>99.9%) | 43Ar | (3/2+) | ||
β−, n (<.1%) | 42Ar | ||||||||
44Cl | 17 | 27 | 43.97812(15) | 0.56(11) s | β− (92%) | 44Ar | (2-) | ||
β−, n (8%) | 43Ar | ||||||||
45Cl | 17 | 28 | 44.98039(15) | 413(25) ms | β− (76%) | 45Ar | (3/2+) | ||
β−, n (24%) | 44Ar | ||||||||
46Cl | 17 | 29 | 45.98512(22) | 232(2) ms | β−, n (60%) | 45Ar | 2-# | ||
β− (40%) | 46Ar | ||||||||
47Cl | 17 | 30 | 46.98950(43)# | 101(6) ms | β− (97%) | 47Ar | 3/2+# | ||
β−, n (3%) | 46Ar | ||||||||
48Cl | 17 | 31 | 47.99541(54)# | 100# ms [>200 ns] | β− | 48Ar | |||
49Cl | 17 | 32 | 49.00101(64)# | 50# ms [>200 ns] | β− | 49Ar | 3/2+# | ||
50Cl | 17 | 33 | 50.00831(64)# | 20# ms | β− | 50Ar | |||
51Cl | 17 | 34 | 51.01534(75)# | 2# ms [>200 ns] | β− | 51Ar | 3/2+# | ||
52Cl[6] | 17 | 35 | β− | 52Ar | |||||
- ^ mCl – Excited nuclear isomer.
- ^ ( ) – Uncertainty (1σ) is given in concise form in parentheses after the corresponding last digits.
- ^ # – Atomic mass marked #: value and uncertainty derived not from purely experimental data, but at least partly from trends from the Mass Surface (TMS).
- ^ a b # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
- ^
Modes of decay:
IT: Isomeric transition n: Neutron emission p: Proton emission - ^ Bold symbol as daughter – Daughter product is stable.
- ^ ( ) spin value – Indicates spin with weak assignment arguments.
- ^ Used in radiodating water
- ^ Cosmogenic nuclide
Main article: Chlorine-36
Trace amounts of radioactive 36Cl exist in the environment, in a ratio of about 7×10−13 to 1 with stable isotopes. 36Cl is produced in the atmosphere by spallation of 36Ar by interactions with cosmic ray protons. In the subsurface environment, 36Cl is generated primarily as a result of neutron capture by 35Cl or muon capture by 40Ca. 36Cl decays to either 36S (1.9%) or to 36Ar (98.1%), with a combined half-life of 308,000 years. The half-life of this hydrophilic nonreactive isotope makes it suitable for geologic dating in the range of 60,000 to 1 million years. Additionally, large amounts of 36Cl were produced by neutron irradiation of seawater during atmospheric detonations of nuclear weapons between 1952 and 1958. The residence time of 36Cl in the atmosphere is about 1 week. Thus, as an event marker of 1950s water in soil and ground water, 36Cl is also useful for dating waters less than 50 years before the present. 36Cl has seen use in other areas of the geological sciences, forecasts, and elements. In chloride-based molten salt reactors the production of 36
Cl by neutron capture is an inevitable consequence of using natural isotope mixtures of chlorine (i.e. Those containing 35
Cl). This produces a long lived radioactive product which has to be stored or disposed off. Isotope separation to produce pure 37
Cl can vastly reduce 36
Cl production, but a small amount might still be produced by (n,2n) reactions involving fast neutrons.
Main article: Chlorine-37
Stable chlorine-37 makes up about 24.23% of the naturally occurring chlorine on earth. Variation occurs as chloride mineral deposits have a slightly elevated chlorine-37 balance over the average found in sea water and halite deposits.[citation needed]
- ^ "Standard Atomic Weights: Chlorine". CIAAW. 2009.
- ^ Meija, Juris; et al. (2016). "Atomic weights of the elements 2013 (IUPAC Technical Report)". Pure and Applied Chemistry. 88 (3): 265–91. doi:10.1515/pac-2015-0305.
- ^ Half-life, decay mode, nuclear spin, and isotopic composition is sourced in:
Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017). "The NUBASE2016 evaluation of nuclear properties" (PDF). Chinese Physics C. 41 (3): 030001. Bibcode:2017ChPhC..41c0001A. doi:10.1088/1674-1137/41/3/030001. - ^ Wang, M.; Audi, G.; Kondev, F. G.; Huang, W. J.; Naimi, S.; Xu, X. (2017). "The AME2016 atomic mass evaluation (II). Tables, graphs, and references" (PDF). Chinese Physics C. 41 (3): 030003-1–030003-442. doi:10.1088/1674-1137/41/3/030003.
- ^ a b c Mukha, I.; et al. (2018). "Deep excursion beyond the proton dripline. I. Argon and chlorine isotope chains". Physical Review C. 98 (6): 064308–1—064308–13. arXiv:1803.10951. doi:10.1103/PhysRevC.98.064308.
- ^ Neufcourt, L.; Cao, Y.; Nazarewicz, W.; Olsen, E.; Viens, F. (2019). "Neutron drip line in the Ca region from Bayesian model averaging". Physical Review Letters. 122: 062502–1—062502–6. arXiv:1901.07632. doi:10.1103/PhysRevLett.122.062502.
- Chlorine isotopes data from The Berkeley Laboratory Isotopes Project's
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