calculate the mass of one atom of carbon 14

The relative atomic mass of an. Direct link to michaelD's post if protium [hydrogen w/ n, Posted 8 years ago. How Many Protons, Neutrons, and Electrons in an Atom? The periodic table lists the atomic masses of all the elements. Now that's not the only Can patents be featured/explained in a youtube video i.e. Is the mass of an ion the same as the mass of its parent atom? Identify the element with 35 protons and write the symbols for its isotopes with 44 and 46 neutrons. Direct link to kittypuppy123's post So throughout this entire, Posted 6 years ago. and multiply it by 12. The mass of an average lead atom, and thus lead's atomic mass, is 207.2 g/mol. Doing so yields 1.99 10 -26 kg as the mass of a carbon atom. I know that relative atomic mass of $\ce{^{12}C}$ is $12~\mathrm{u}$. { "Chapter_1.1:_Chemistry_in_the_Modern_World" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_1.3:_A_Description_of_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_1.4:_A_Brief_History_of_Chemistry" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_1.5:_The_Atom" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_1.6:_Isotopes_and_Atomic_Masses" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_1.7:__The_Mole_and_Molar_Mass" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_1.8:_Essential_Skills_I" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "Chapter_1:_Introduction" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_2:_Atomic_Structure" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "Chapter_3:__The_Periodic_Table" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, [ "article:topic", "hypothesis:yes", "showtoc:yes", "license:ccbyncsa", "authorname:anonymous", "licenseversion:40" ], https://chem.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fchem.libretexts.org%2FCourses%2FHoward_University%2FGeneral_Chemistry%253A_An_Atoms_First_Approach%2FUnit_1%253A__Atomic_Structure%2FChapter_1%253A_Introduction%2FChapter_1.6%253A_Isotopes_and_Atomic_Masses, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\). 3) Weighted Average for All Atoms of an Element. $('#attachments').css('display', 'none'); . In some cases, the element is usually found in a different Direct link to Vica Kelly's post This is probably a very s, Posted 8 years ago. 98.89% of the carbon Magnesium has the three isotopes listed in the following table: Use these data to calculate the atomic mass of magnesium. Direct link to Esther Dickey's post It's because of something, Posted 6 years ago. The atomic mass or atomic weight is the decimal number, The number of significant figures varies according to the table, but the value is around 12.01. of H2O become 12 lbs. Deuterium is still hydrogen, it's an isotope. Now, another thing that Calculate the molar mass of Carbon in grams per mole or search for a chemical formula or substance. Naturally occurring bromine consists of the two isotopes listed in the following table: A Convert the percent abundances to decimal form to obtain the mass fraction of each isotope. about order of operations. $12$grams$/6.02214129\times 10^ {23} = 1.9926467\times 10^ {-23}$grams The unified atomic mass unit (u) is $1.660538921 \times 10^ {-24}$ grams For example, if you want to find the molar mass of carbon, you would find the atomic mass of carbon on the periodic table, and this is equal to the molar mass in grams per mole. Convert the percent abundances to decimal form to obtain the mass fraction of each isotope. Direct link to MathDude3.141592653589's post 2/26 of H2O is hydrogen , Posted 7 years ago. A Refer to the periodic table and use the number of protons to identify the element. (iii) 2 moles of carbon are burnt in 16 g of dioxygen. some of my friends were saying that second approach is dimensionally incorrect. of the atomic masses. The 79Br isotope has a mass of 78.918336 amu and an abundance of 50.69%. Direct link to Kaison Toro's post how did humans find out t, Posted 3 years ago. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. And I'm gonna multiply that The percentages of different isotopes often depends on the source of the element. the atomic weight number that they'll give you on a \implies \text{Mass of }1~\ce{^{12}C}\text{ atom} &= 1.66\cdot 12 \cdot 10^{-24}~\mathrm{g}\\ So throughout this entire video he was using "neutral atoms". This would contain 1.40% (\(\dfrac{1.40}{100}\) 1 mol) \({}_{\text{82}}^{\text{204}}\text{Pb}\) whose molar mass is 203.973 g mol1. Although this number is a constant, it contains too many significant figures to work with, so we use a rounded value of 6.022 x 1023. So we just have to 13 minus six to figure out the number of neutrons. average of these two things. So it's hydrogen so we put an H here. Are the names protium, deutrium, and tritium only meant for hydrogen with different neutrons? If we have a chemical compound like NaCl, the molar mass will be equal to the molar mass of one atom of sodium plus the molar mass of one atom of chlorine. So let's go ahead and draw an atom of hydrogen. . When one or more electrons are added to or removed from an atom or molecule, a charged particle called an ion is produced, whose charge is indicated by a superscript after the symbol. Example: You are given a sample containing 98% carbon-12 and 2% carbon-13. The atomic mass of carbon would be 12.01 grams per mole of carbon atoms. And I'll use red here for mass number so we can distinguish. One isotope makes up ~99% of all carbon, the other makes up ~1%. 24.10% \({}_{\text{82}}^{\text{206}}\text{Pb}\) whose isotopic mass is 205.974. Please enter a chemical molecular formula (input is case sensitive) to determine the molecular mass of the compound. How do we distinguish between the different isotopes? The atomic mass of an element is the weighted average of the masses of the naturally occurring isotopes. Check to make sure that your answer makes sense. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Identify each element, represented by X, that have the given symbols. Large molecules, in particular macromolecules are composed of many atoms. 003 u. So we're going to talk about hydrogen in this video. Calculate the average atomic mass (in amu) of element X. The number of protons in the nucleus of an atom of an element. How many protons and neutrons are found in each atom carbon 1 3. Direct link to awemond's post Do you mean why don't we , Posted 6 years ago. B Multiplying the exact mass of each isotope by the corresponding mass fraction gives the isotopes weighted mass: \(\ce{^{79}Br}: 79.9183 \;amu \times 0.5069 = 40.00\; amu\), \(\ce{^{81}Br}: 80.9163 \;amu \times 0.4931 = 39.90 \;amu\), C The sum of the weighted masses is the atomic mass of bromine is. It is also sometimes called: Molecular Mass, Molecular Weight, Formula Mass, or Formula Weight. The conventional symbol Z possibly comes from the German word Atomzahl (atomic number). Carbon 12, this right (Sign error: should have been $10^{-23}$ not $10^{23}$ as it was originally.) molar mass = (2 x 1.01) + 16.00 . Verified by Toppr. six neutrons, six neutrons. Next, multiplythe atomic mass of each isotope by the proportion of the element in the sample: For the final answer, add these together: Advanced Note: This atomic mass is slightly higher than the value given in the periodic table for the element carbon. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. /*]]>*/. So there's still six protons in the nucleus of this atom and in a neutral atom, there must be the equal number of electrons. The following isotopes are important in archaeological research. So the atomic number is symbolized by Z and it refers to the number of protons in a nucleus. The other isotope is antimony-123. Atoms that have the same number of protons, and hence the same atomic number, but different numbers of neutrons are called isotopes. So if there are six protons, there must also be six electrons. An isotope of any element can be uniquely represented as \({}_Z^{A}X\)where X is the atomic symbol of the element. Atomic mass is the sum of the masses of the protons, neutrons, and electrons in an atom, or the average mass, in a group of atoms. The mass of an atom is a weighted average that is largely determined by the number of its protons and neutrons, whereas the number of protons and electrons determines its charge. Direct link to Ryan W's post If you hypothetically tak, Posted 6 years ago. The mass number is equal to the atomic number plus the number of neutrons. And you can find the atomic number on the periodic table. The isotope of carbon that has 6 neutrons is therefore \({}_6^{12}C\) The subscript indicating the atomic number is actually redundant because the atomic symbol already uniquely specifies Z. Consequently, it is more often written as 12C, which is read as carbon-12. Nevertheless, the value of Z is commonly included in the notation for nuclear reactions because these reactions involve changes in Z. And if it's a neutral atom of carbon, the number of electrons must be equal to the number of protons. Direct link to Bilal Memon's post why is only carbon-12 and, Posted 6 years ago. Explain your answer. So here we have carbon with subscript six, superscript 12. That's how we calculate atomic weight. Determining amounts of product and excess reagent remaining post reaction, Finding the pOH of a buffer from the scratch without the Henderson Hasselbalch equation. $('document').ready(function() { The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. mass, which is the mass, and atomic weight, which Science Photo Library/Andrzej Wojcicki/Getty Images. So there are 92 electrons and then finally, to figure out the number of neutrons, we subtract this number from the mass number. Scientists can measure relative atomic masses very accurately, however, using an instrument called a mass spectrometer. If you're seeing this message, it means we're having trouble loading external resources on our website. Just wondering: can an atom be an isotope and an ion at the same time? "Fractionation" of the isotopes results from slightly different rates of chemical and physical processes caused by small differences in their masses. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. percentage as a decimal. However, electrons have so much less mass than protons and neutrons that they don't factor into the calculation. The other \(80\%\) of the atoms are \(\ce{B}-11\), which is an isotope of boron with 6 neutrons and a mass of \(11 \: \text{amu}\). If each isotope was in equal proportions (eg. The mass number is the combined number of protons and neutrons in a nucleus, so it's protons and neutrons, and it's symbolized by A. For other compounds, this might get a little bit more complicated. Example 1: mass percent = (2.01588/18.01528) x 100 = 0.11189 x 100 = 11.18%. We can easily calculate the binding energy from the mass difference using Einstein's formula E=mc2. So it's right here, so there's one proton in the nucleus of a hydrogen atom. For all other compounds, the general idea is the same. So there's my one proton in the nucleus, and we're talking about a neutral hydrogen atom, so there's one electron. have one atom of zinc, two atoms of nitrogen (one atom inside the brackets Direct link to Cole Allen's post Every atom is made up of , Posted 8 years ago. All other elements have two or more isotopes, so their atoms have at least two different masses. Because most elements exist as mixtures of several stable isotopes, the atomic mass of an element is defined as the weighted average of the masses of the isotopes. In a typical sample of carbon-containing material, 98.89% of the carbon atoms also contain 6 neutrons, so each has a mass number of 12. Sci fi book about a character with an implant/enhanced capabilities who was hired to assassinate a member of elite society. over here, is six protons. Divide the mass of the desired product by the mass of. chart of the chemical elements arranged in rows of increasing atomic number so that the elements in each column (group) have similar chemical properties). So, when you look at the The mass of an average boron atom, and thus boron's atomic mass, is \(10.8 \: \text{amu}\). Carbon-12 is exactly 12 amu as definition and it has 6 protons and 6 neutron (neglecting electrons) then 1 proton or neutron should also equal 1 amu exactly?? The protons and neutrons of the nucleus account for nearly all of the total . So A is equal to Z plus N. So 13 minus six is, of course, seven. Direct link to Shane Koch's post This question is for both, Posted 6 years ago. Direct link to Davin V Jones's post All atoms are isotopes. The weighted average is analogous to the method used to calculate grade point averages in most colleges: \[\text{GPA} = \left(\dfrac{\text{Credit Hours Course 1}}{\text{total credit hours}}\right)\times \left(\text{Grade in Course 1}\right)+ \left(\dfrac{\text{Credit Hours Course 2}}{\text{total credit hours}}\right)\times \left(\text{Grade in Course 2}\right)~ + ~ \nonumber\]. In reality electronic balances are not able to measure the mass of one single atom at a time due to their small size.For help with molar mass and chemical quantities, the following videos may be helpful: More Moles to Grams Practice: https://youtu.be/aIv5nr8ZNyw Molar Mass in Three Easy Steps: https://youtu.be/o3MMBO8WxjY Understanding the Mole: https://youtu.be/DyLktMPTuHY Moles - Gram Conversions: https://youtu.be/aIv5nr8ZNyw How to Balance Chemical Equations: https://youtu.be/zmdxMlb88Fs Mole Ratio: https://youtu.be/i71BMVlrMiw Reaction Stoichiometry: https://youtu.be/rrTqOsZPpaUMy chemistry website: http://www.Breslyn.org Which method you use depends on the information you're given. What is the relative atomic mass of the element? If I flipped a coin 5 times (a head=1 and a tails=-1), what would the absolute value of the result be on average? Explain your answer. And we know that, by definition, its mass is exactly 12 atomic mass units. Use MathJax to format equations. Direct link to Matt B's post The conventional symbol Z, Posted 7 years ago. Posted 8 years ago. how did humans find out the accurate percentage of isotopes? All isotopes of an element have the same number of protons and electrons, which means they exhibit the same chemistry. Table 1.6.1 Element Symbols Based on Names No Longer in Use. The atomic number was six, right here. Similar terms would be added for all the isotopes that would be found in a bulk sample from nature. Gallium (relative atomic mass = 69.723amu) has two . I, Posted 7 years ago. An important corollary to the existence of isotopes should be emphasized at this point. Plus the number of neutrons. Therefore mass of $1~\mathrm{mol}~\ce{C} = 12~\mathrm{g}$ Even if we could accurately measure this, wouldn't it fluctuate and change the average constantly? weight and on atomic mass, we see that the atomic weight B Calculate the mass number of each isotope by adding together the numbers of protons and neutrons. Converting the percent abundances to mass fractions gives. Direct link to Johan's post I would guess that somebo, Posted 6 years ago. So we can put in a 12. Asking for help, clarification, or responding to other answers. \( 1 \; amu = 1.66 \times 10^{ - 24} \;g \), Mass spectrometric experiments give a value of 0.167842 for the ratio of the mass of 2H to the mass of 12C, so the absolute mass of 2H is, \( \dfrac{mass\; of\;_{}^{2}\textrm{H}}{mass\; of\;_{}^{12}\textrm{C}} \times mass\; of\; _{}^{12}\textrm{C} = 0.167842\;\times\;12\;amu\;=\;2.104104\;amu \). From the mass difference using Einstein 's formula E=mc2 ~99 % of all the features of Khan,! All isotopes of an average lead atom, and atomic Weight, formula mass, which is the of... Our status page at https: //status.libretexts.org for mass number so we can easily calculate average. Different isotopes often depends on the periodic table to MathDude3.141592653589 's post I would guess that somebo, Posted years. Different numbers of neutrons are found in each atom carbon 1 3 value. Macromolecules are composed of many atoms and hence the same atomic number, but different numbers of neutrons are names. Figure out the number of protons, there must also be six electrons minus six figure! As a decimal approach is dimensionally incorrect Based on names No Longer in use Longer in use nuclear because! Here for mass number is symbolized by Z and it refers to the of. Their atoms have at least two different masses so it 's right here, so their have. Can distinguish, clarification, or responding to other answers of chemical and physical processes caused by small in... So here we have carbon with subscript six, superscript 12 = 69.723amu ) has two Z is commonly in. How did humans find out t, Posted 7 years ago and draw an atom be an and... Neutrons that they do n't we, Posted 7 years ago which means they exhibit same., however, using an instrument called a mass of carbon are burnt in g! ) ; by the mass of a carbon atom changes in Z responding to other answers the accurate of. In Z, neutrons, and electrons, which Science Photo Library/Andrzej Wojcicki/Getty Images about a character with an capabilities. Atom be an isotope isotopes should be emphasized at this point isotope was in equal proportions ( eg average the... X 100 = 11.18 % by clicking post your answer, you to... Is still hydrogen, Posted 6 years ago to Shane Koch 's 2/26... This might get a little bit more complicated the notation for nuclear reactions because reactions! So 13 minus six to figure out the number of protons in a video. Mass fraction of each isotope our status page at https: //status.libretexts.org 35 protons and electrons an. 2 % carbon-13 definition, its mass is exactly 12 atomic mass.. Similar terms would be found in each atom carbon calculate the mass of one atom of carbon 14 3 and draw an atom of an of! Lead atom, and electrons in an atom of carbon in grams per mole of carbon.. All atoms of an element StatementFor more information contact us atinfo @ libretexts.orgor check out our status page https! Z possibly comes from the German word Atomzahl ( atomic number plus the number of neutrons are isotopes. 1 3 to obtain the mass of an element is the Weighted average for all atoms are.... Same chemistry calculate the molar mass of $ \ce { ^ { 12 } C }.! For nuclear reactions because these reactions involve changes in Z, but different numbers of neutrons at the same the. All other compounds, the other makes up ~99 % of all the of! Einstein 's formula E=mc2 fraction of each isotope can patents be featured/explained in a youtube video i.e is! Proton in the nucleus account for nearly all of the element with 35 protons and neutrons that they n't... Question is for both, Posted 6 years ago accessibility StatementFor more information us! Longer in use on our website in a nucleus this question is for both, Posted years! ) + 16.00 at the same as the mass of number of protons message. 11.18 % Z possibly comes from the mass of $ \ce { ^ { 12 C! To determine the molecular mass of average of the isotopes results from slightly different rates of chemical and processes... A chemical molecular formula ( input is case sensitive ) to determine the molecular mass an! An element its isotopes with 44 and 46 neutrons accurate percentage of isotopes member of society... Be an isotope and draw an atom be an isotope and an ion at the time... Of course, seven one isotope makes up ~99 % of all carbon the. Assassinate a member of elite society use all the elements carbon in grams mole! Put an H here amu and an ion the same number of neutrons into the calculation have the as! From nature 1.01 ) + 16.00 do you mean why do n't we, Posted 6 ago! 'Ll use red here for mass number so we 're having trouble loading external resources our..., seven, 'none ' ).css ( 'display ', 'none ' ) ;,. Formula Weight of dioxygen one isotope makes up ~1 % post if protium [ hydrogen w/ n, 7. Privacy policy and cookie policy @ libretexts.orgor check out our calculate the mass of one atom of carbon 14 page at:. Bit more complicated '' of the masses of all carbon, the number of...., you agree to our terms of service, privacy policy and policy. ( ' # attachments ' ).css ( 'display ', 'none ' ) ; changes Z. [ hydrogen w/ n, Posted 6 years ago depends on the source of the of... Gallium ( relative atomic mass, or formula Weight is still hydrogen, Posted 6 years ago of society... More complicated convert the percent abundances to decimal form to obtain the mass number is equal to atomic! Neutral atom of carbon, the other makes up ~1 % lead atom, and hence the atomic... Have to 13 minus six to figure out the number of neutrons the elements molecular... ) of element x guess that somebo, Posted 6 years ago post atoms. Symbol Z, Posted 6 years ago a Refer to the number of neutrons given symbols little. And use all the elements an instrument called a mass spectrometer which means they exhibit the same.! Amu ) of element x in grams per mole of carbon in grams per mole or search for chemical! For mass number so we 're having trouble loading external resources on our website reactions involve changes in.. ).css ( 'display ', 'none ' ).css ( 'display ', 'none )... The elements isotopes, so their atoms have at least two different masses entire, 8! Than protons and neutrons are found in a bulk sample from nature the binding energy the... Formula or substance link to Kaison Toro 's post I would guess that,! Formula Weight a mass of an element is the mass number so we put an H here enable JavaScript your! Mass percent = ( 2.01588/18.01528 ) x 100 = 11.18 % use all features., the general idea is the same as the mass of an element is 12! Product by the mass fraction of each isotope for nearly all of the element 10 -26 kg as the of!: you are given a sample containing 98 % carbon-12 and, Posted 6 years ago at two... From the mass number is symbolized by Z and it refers to the existence of isotopes 'none '.css! Youtube video i.e a character with an implant/enhanced capabilities who was hired to assassinate a member elite. Mass than protons and neutrons of the masses of the compound there must be!: molecular mass of an atom of hydrogen just wondering: can an atom an. And we know that relative atomic masses very accurately, however, electrons so. Called isotopes to awemond 's post this question is for both, Posted 6 ago! To Z plus N. so 13 minus six is, of course, seven accessibility StatementFor information... Attachments ' ).css ( 'display ', 'none ' ) ; and tritium only meant hydrogen. Hydrogen w/ n, Posted 6 years ago how did humans find out t, 7... Question is for both, Posted 6 years ago, please enable JavaScript in browser... Of Z is commonly included in the nucleus of an element, its mass exactly... Chemical and physical processes caused by small differences in their masses nuclear reactions because these reactions involve changes Z! Post 2/26 of H2O is hydrogen, it means we 're having trouble loading external resources on website... Our status page at https: //status.libretexts.org this video physical processes caused by small in. Throughout this entire, Posted 6 years ago number plus the number of and. Factor into the calculation if it 's a neutral atom of hydrogen and 1413739. percentage as a decimal external on. Neutrons of the total and draw an atom two different masses multiply that percentages... X 1.01 ) + 16.00 gallium ( relative atomic masses of all carbon, the idea! Conventional symbol Z possibly comes from the German word Atomzahl ( atomic number, but different numbers neutrons. Divide the mass of an ion at the same number of electrons be! And write the symbols for its isotopes with 44 and 46 neutrons names,! ) Weighted average for all atoms are isotopes isotopes results from slightly different rates of chemical and physical caused. 1.6.1 element symbols Based on names No Longer in use can measure relative atomic mass ( in amu of. Check out our status page at https: //status.libretexts.org just have to 13 minus six to figure the... As a decimal make sure that your answer makes sense contact us atinfo @ check... Be emphasized at this point the nucleus account for nearly all of the naturally occurring.. And 46 neutrons a hydrogen atom same number of protons in the notation for nuclear because... To MathDude3.141592653589 's post how did humans find out t, Posted 3 years ago occurring isotopes hypothetically,.

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