How to find isotopes of chlorine

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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.

Table \(\PageIndex{1}\): Atomic Masses and Percents of Abundance of Some Natural Isotopes
Element Isotope (Symbol) Percent Natural Abundance Atomic Mass \(\left( \text{amu} \right)\) Average Atomic Mass \(\left( \text{amu} \right)\)
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.

  1. Define atomic mass.
  2. What information do you need to calculate atomic mass for an element?
  3. Calculate the atomic mass for carbon using the data provided in the table below.

Isotope

Atomic Mass

Percent Abundance

carbon-12

12.000000

98.90

carbon-13

13.003355

1.100

How to find isotopes of chlorine

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How to find isotopes of chlorine

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.

Main isotopes of chlorine (17Cl)
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
Standard atomic weight Ar°(Cl)

  • [35.44635.457]
  • 35.45±0.01 (abridged)[1][2]

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Nuclide[3]
[n 1]
Z N Isotopic mass (Da)[4]
[n 2][n 3]
Half-life
[n 4]
Decay
mode
[n 5]
Daughter
isotope
[n 6]
Spin and
parity
[n 7][n 4]
Natural abundance (mole fraction)
Excitation energy Normal proportion Range of variation
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
This table header & footer:
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  1. ^ mCl – Excited nuclear isomer.
  2. ^ ( ) – Uncertainty (1σ) is given in concise form in parentheses after the corresponding last digits.
  3. ^ # – Atomic mass marked #: value and uncertainty derived not from purely experimental data, but at least partly from trends from the Mass Surface (TMS).
  4. ^ a b # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
  5. ^ Modes of decay:
    IT: Isomeric transition
    n: Neutron emission
    p: Proton emission
  6. ^ Bold symbol as daughter – Daughter product is stable.
  7. ^ ( ) spin value – Indicates spin with weak assignment arguments.
  8. ^ Used in radiodating water
  9. ^ Cosmogenic nuclide

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.

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]

  1. ^ "Standard Atomic Weights: Chlorine". CIAAW. 2009.
  2. ^ 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.
  3. ^ 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ 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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