Chlorine's Mass Is 35.5, and No Chlorine Atom Weighs That
Learn the Bohr-Bury rules for filling shells, how to read valency from the outermost shell, how isotopes differ from isobars, and how to calculate an average atomic mass from abundances.
Why is chlorine's atomic mass 35.5 when no atom can weigh half a unit?
Because describes a mixture, not an atom.
Every individual chlorine atom has a whole-number mass number — either or . Naturally occurring chlorine is a mixture of the two, in which about three quarters of the atoms are the lighter kind. Averaging over the mixture:
So u is the mass of an average chlorine atom in a sample, and it is the figure that appears in the periodic table. It is not the mass of any real atom you could pick out.
That is also why one of Dalton's postulates had to go. Atoms of the same element are not all identical in mass — and the atoms that differ are called isotopes. This page covers the third part of the CBSE Class 9 Science chapter on the journey inside the atom.
Every individual chlorine atom has a whole-number mass number — either or . Naturally occurring chlorine is a mixture of the two, in which about three quarters of the atoms are the lighter kind. Averaging over the mixture:
So u is the mass of an average chlorine atom in a sample, and it is the figure that appears in the periodic table. It is not the mass of any real atom you could pick out.
That is also why one of Dalton's postulates had to go. Atoms of the same element are not all identical in mass — and the atoms that differ are called isotopes. This page covers the third part of the CBSE Class 9 Science chapter on the journey inside the atom.
What are the Bohr-Bury rules for filling electron shells?
Three rules decide how electrons are distributed among the shells.
- The maximum number of electrons a shell can hold is ****, where is the shell number. So K () holds , L () holds , M () holds , and N () holds .
- The outermost shell can never hold more than ** electrons.
- Shells are filled stepwise from the innermost outward; a new shell begins only when the previous one holds as many electrons as these rules allow.
Worked configurations up to atomic number .**
- Hydrogen ():
- Helium ():
- Lithium ():
- Carbon ():
- Nitrogen ():
- Oxygen ():
- Fluorine ():
- Neon ():
- Sodium ():
- Magnesium ():
- Aluminium ():
- Silicon ():
- Phosphorus ():
- Sulphur ():
- Chlorine ():
- Argon ():
- Potassium ():
- Calcium ():
The two cases everything turns on. Potassium has electrons. The M shell could hold , so looks reasonable — and it is wrong, because the outermost shell may not exceed . Once the M shell reaches , the nineteenth electron must start the N shell, giving .
Calcium () is the same story: ****, not .
**So the rule and the outermost-shell rule can disagree, and the outermost-shell rule wins. That is the single most examined point in this section, and potassium and calcium are the two elements where it bites within the Class 9 range.
Everyday consequence.** Because sodium () and potassium () both end with a single outermost electron, they behave chemically alike — both are very reactive metals forming ions with a single positive charge. The outermost shell decides chemical behaviour, which is why the configuration is worth writing out before anything else is asked.
- The maximum number of electrons a shell can hold is ****, where is the shell number. So K () holds , L () holds , M () holds , and N () holds .
- The outermost shell can never hold more than ** electrons.
- Shells are filled stepwise from the innermost outward; a new shell begins only when the previous one holds as many electrons as these rules allow.
Worked configurations up to atomic number .**
- Hydrogen ():
- Helium ():
- Lithium ():
- Carbon ():
- Nitrogen ():
- Oxygen ():
- Fluorine ():
- Neon ():
- Sodium ():
- Magnesium ():
- Aluminium ():
- Silicon ():
- Phosphorus ():
- Sulphur ():
- Chlorine ():
- Argon ():
- Potassium ():
- Calcium ():
The two cases everything turns on. Potassium has electrons. The M shell could hold , so looks reasonable — and it is wrong, because the outermost shell may not exceed . Once the M shell reaches , the nineteenth electron must start the N shell, giving .
Calcium () is the same story: ****, not .
**So the rule and the outermost-shell rule can disagree, and the outermost-shell rule wins. That is the single most examined point in this section, and potassium and calcium are the two elements where it bites within the Class 9 range.
Everyday consequence.** Because sodium () and potassium () both end with a single outermost electron, they behave chemically alike — both are very reactive metals forming ions with a single positive charge. The outermost shell decides chemical behaviour, which is why the configuration is worth writing out before anything else is asked.
How do you find an element's valency from its configuration?
Count the electrons in the outermost shell, then ask how far the atom is from a full one.
The electrons in the outermost shell are the valence electrons, and valency is the combining capacity — the number of electrons the atom must lose, gain or share to reach a stable arrangement.
The rule follows from taking the shorter route:
- If the valence electrons number ** or fewer, the atom loses them, and the valency equals the number of valence electrons
- If they number more than , the atom gains the few it needs, and the valency is minus the number of valence electrons
Worked examples — losing electrons.**
- Sodium (): valence electron, so **valency **
- Magnesium (): **valency **
- Aluminium (): **valency **
- Carbon (): **valency
Worked examples — gaining electrons.**
- Nitrogen (): **valency **
- Oxygen (): **valency **
- Chlorine (): **valency
The noble gases.** Helium () has a complete first shell; neon () and argon () have complete outer octets. They need neither to lose nor to gain, so their **valency is — and that is precisely why they form almost no compounds and are described as inert.
Everyday evidence.** Sodium has valency and chlorine has valency , so they combine one atom to one, giving — common salt. Magnesium has valency and chlorine , so two chlorines are needed for each magnesium, giving . The valencies predict the formula, and that is what makes them worth calculating.
**Why is the dividing line.** An atom with valence electrons would need more to complete an octet, and losing is the shorter route. An atom with would need to lose or gain , and gaining is shorter. At exactly , losing and gaining are equally far, which is why carbon shares instead — and sharing is the basis of the enormous number of carbon compounds.
Valency is about the outermost shell alone. The inner shells play no part. That is why sodium and potassium, with quite different total electron counts of and , have the same valency of — they both end in a single outermost electron, and nothing else matters.
The electrons in the outermost shell are the valence electrons, and valency is the combining capacity — the number of electrons the atom must lose, gain or share to reach a stable arrangement.
The rule follows from taking the shorter route:
- If the valence electrons number ** or fewer, the atom loses them, and the valency equals the number of valence electrons
- If they number more than , the atom gains the few it needs, and the valency is minus the number of valence electrons
Worked examples — losing electrons.**
- Sodium (): valence electron, so **valency **
- Magnesium (): **valency **
- Aluminium (): **valency **
- Carbon (): **valency
Worked examples — gaining electrons.**
- Nitrogen (): **valency **
- Oxygen (): **valency **
- Chlorine (): **valency
The noble gases.** Helium () has a complete first shell; neon () and argon () have complete outer octets. They need neither to lose nor to gain, so their **valency is — and that is precisely why they form almost no compounds and are described as inert.
Everyday evidence.** Sodium has valency and chlorine has valency , so they combine one atom to one, giving — common salt. Magnesium has valency and chlorine , so two chlorines are needed for each magnesium, giving . The valencies predict the formula, and that is what makes them worth calculating.
**Why is the dividing line.** An atom with valence electrons would need more to complete an octet, and losing is the shorter route. An atom with would need to lose or gain , and gaining is shorter. At exactly , losing and gaining are equally far, which is why carbon shares instead — and sharing is the basis of the enormous number of carbon compounds.
Valency is about the outermost shell alone. The inner shells play no part. That is why sodium and potassium, with quite different total electron counts of and , have the same valency of — they both end in a single outermost electron, and nothing else matters.
How do isotopes differ from isobars?
Isotopes are the same element with different masses; isobars are different elements with the same mass number.
Isotopes — atoms of the same element, so the same atomic number , but different mass numbers because they contain different numbers of neutrons.
- Hydrogen has three: protium with neutrons, deuterium with , and tritium with
- Carbon: and , with and neutrons
- Chlorine: and , with and neutrons
Isobars — atoms of different elements, so different atomic numbers, which happen to have the same mass number.
- Calcium and argon — both , with and neutrons
- Carbon and nitrogen — both
How to classify a given pair in one step. Compare the bottom numbers. Same means isotopes; different with the same means isobars.
- and : same , so isotopes
- and : same , different , so isobars
- and : isotopes
- and : isobars
Properties of isotopes. They have identical chemical properties but different physical properties.
The chemistry is identical because chemistry depends on the electrons, and isotopes of one element have the same atomic number and therefore the same electronic configuration. The physical properties differ because the masses differ.
A consequence worth drawing out. Because their chemistry is identical, isotopes cannot be separated by any chemical method — no reaction treats one differently from the other. Separating them needs a method that works on mass alone, which is a physical process, not a chemical one.
Isotopes are why one of Dalton's postulates failed. He held that all atoms of an element are identical in mass. Chlorine's two forms show otherwise, and that is exactly what makes an average atomic mass necessary — which is the last section of this page.
Isotopes — atoms of the same element, so the same atomic number , but different mass numbers because they contain different numbers of neutrons.
- Hydrogen has three: protium with neutrons, deuterium with , and tritium with
- Carbon: and , with and neutrons
- Chlorine: and , with and neutrons
Isobars — atoms of different elements, so different atomic numbers, which happen to have the same mass number.
- Calcium and argon — both , with and neutrons
- Carbon and nitrogen — both
How to classify a given pair in one step. Compare the bottom numbers. Same means isotopes; different with the same means isobars.
- and : same , so isotopes
- and : same , different , so isobars
- and : isotopes
- and : isobars
Properties of isotopes. They have identical chemical properties but different physical properties.
The chemistry is identical because chemistry depends on the electrons, and isotopes of one element have the same atomic number and therefore the same electronic configuration. The physical properties differ because the masses differ.
A consequence worth drawing out. Because their chemistry is identical, isotopes cannot be separated by any chemical method — no reaction treats one differently from the other. Separating them needs a method that works on mass alone, which is a physical process, not a chemical one.
Isotopes are why one of Dalton's postulates failed. He held that all atoms of an element are identical in mass. Chlorine's two forms show otherwise, and that is exactly what makes an average atomic mass necessary — which is the last section of this page.
Formula
How do you calculate an average atomic mass from abundances?
Weight each isotope's mass number by how common it is:
Worked example 1 — chlorine. Naturally occurring chlorine is about and .
which is the value printed in the periodic table.
Worked example 2 — carbon. A sample is and .
Worked example 3 — boron. Boron is about and .
Worked example 4 — neon. A sample is and .
Worked example 5 — working backwards. An element has isotopes of mass number and , and an average atomic mass of u. Find the percentage of each.
Let the lighter isotope be , so the heavier is :
So of the lighter isotope and of the heavier — matching worked example 4, as it must.
The average always lies between the two mass numbers, and closer to the more abundant one. Chlorine's sits between and and nearer , because is commoner. An answer outside that range is wrong before anything else is checked.
Applications of isotopes, as the syllabus lists them:
- An isotope of uranium is used as fuel in nuclear reactors
- An isotope of cobalt is used in the treatment of cancer
- An isotope of iodine is used in the treatment of goitre
The average is usually not a whole number, and that is the point. Every individual atom has a whole-number mass number, so u describes no chlorine atom in existence. It describes the sample — which is exactly the quantity a chemist weighing out chlorine actually needs, because a real sample is always the mixture.
Worked example 1 — chlorine. Naturally occurring chlorine is about and .
which is the value printed in the periodic table.
Worked example 2 — carbon. A sample is and .
Worked example 3 — boron. Boron is about and .
Worked example 4 — neon. A sample is and .
Worked example 5 — working backwards. An element has isotopes of mass number and , and an average atomic mass of u. Find the percentage of each.
Let the lighter isotope be , so the heavier is :
So of the lighter isotope and of the heavier — matching worked example 4, as it must.
The average always lies between the two mass numbers, and closer to the more abundant one. Chlorine's sits between and and nearer , because is commoner. An answer outside that range is wrong before anything else is checked.
Applications of isotopes, as the syllabus lists them:
- An isotope of uranium is used as fuel in nuclear reactors
- An isotope of cobalt is used in the treatment of cancer
- An isotope of iodine is used in the treatment of goitre
The average is usually not a whole number, and that is the point. Every individual atom has a whole-number mass number, so u describes no chlorine atom in existence. It describes the sample — which is exactly the quantity a chemist weighing out chlorine actually needs, because a real sample is always the mixture.
Exam tip
Exam tip: cap the outermost shell at eight
**Maximum electrons per shell is ** — K , L , M , N — but the **outermost shell never exceeds **, and that rule wins.
So potassium () is ****, not ; and calcium () is ****, not . These are the two elements in range where it matters.
Valency: if valence electrons are or fewer, valency equals them; if more than , valency is ** minus** them.
So sodium , magnesium , aluminium , carbon , nitrogen , oxygen , chlorine — and the **noble gases .
Valency depends on the outermost shell only**, which is why sodium and potassium share a valency of .
Isotopes: same , different . Isobars: different , same . Compare the bottom numbers to classify a pair in one step.
Isotopes have identical chemical and different physical properties, so they cannot be separated chemically.
Average atomic mass , and it must lie between the two mass numbers, nearer the commoner one.
For a backwards question, let the lighter isotope be and the other .
And name the three isotope applications when asked: uranium as reactor fuel, cobalt for cancer treatment, iodine for goitre.
So potassium () is ****, not ; and calcium () is ****, not . These are the two elements in range where it matters.
Valency: if valence electrons are or fewer, valency equals them; if more than , valency is ** minus** them.
So sodium , magnesium , aluminium , carbon , nitrogen , oxygen , chlorine — and the **noble gases .
Valency depends on the outermost shell only**, which is why sodium and potassium share a valency of .
Isotopes: same , different . Isobars: different , same . Compare the bottom numbers to classify a pair in one step.
Isotopes have identical chemical and different physical properties, so they cannot be separated chemically.
Average atomic mass , and it must lie between the two mass numbers, nearer the commoner one.
For a backwards question, let the lighter isotope be and the other .
And name the three isotope applications when asked: uranium as reactor fuel, cobalt for cancer treatment, iodine for goitre.
Did you know
Why heavy water is genuinely different water
Hydrogen's three isotopes are unusual among isotopes in one respect: the mass differences between them are enormous in proportion.
Protium has nucleon, deuterium has , and tritium has . So deuterium is twice as heavy as protium, and tritium three times. Compare that with chlorine, where is heavier than by only about one part in eighteen.
That proportion has a visible consequence. Water made with deuterium instead of ordinary hydrogen is called heavy water, and it is genuinely heavier — noticeably denser than ordinary water, with a slightly higher boiling point and freezing point. Ordinary water and heavy water are chemically the same substance and physically distinguishable, which is the isotope rule from this page made obvious.
For most elements the isotopes are so close in mass that no such difference can be noticed at all. Two samples of chlorine differing in isotopic mixture behave identically in every ordinary measurement, which is why the periodic table can quote a single average and chemists can rely on it.
Heavy water has a practical use that follows from its mass. In some nuclear reactors it is used to slow down neutrons, and it does that job better than ordinary water precisely because of the extra nucleon in each hydrogen — a nucleus of the right mass slows a neutron more effectively than a lighter one.
So hydrogen's isotopes are worth learning by name, and not only because examinations ask for them. They are the one case where the difference between isotopes is large enough to give the substances different everyday properties — and they show clearly why isotopes must be separated by physical rather than chemical means.
Protium has nucleon, deuterium has , and tritium has . So deuterium is twice as heavy as protium, and tritium three times. Compare that with chlorine, where is heavier than by only about one part in eighteen.
That proportion has a visible consequence. Water made with deuterium instead of ordinary hydrogen is called heavy water, and it is genuinely heavier — noticeably denser than ordinary water, with a slightly higher boiling point and freezing point. Ordinary water and heavy water are chemically the same substance and physically distinguishable, which is the isotope rule from this page made obvious.
For most elements the isotopes are so close in mass that no such difference can be noticed at all. Two samples of chlorine differing in isotopic mixture behave identically in every ordinary measurement, which is why the periodic table can quote a single average and chemists can rely on it.
Heavy water has a practical use that follows from its mass. In some nuclear reactors it is used to slow down neutrons, and it does that job better than ordinary water precisely because of the extra nucleon in each hydrogen — a nucleus of the right mass slows a neutron more effectively than a lighter one.
So hydrogen's isotopes are worth learning by name, and not only because examinations ask for them. They are the one case where the difference between isotopes is large enough to give the substances different everyday properties — and they show clearly why isotopes must be separated by physical rather than chemical means.
Exam relevance
How does average atomic mass feed into JEE and NEET Chemistry?
Because the figure is the number every mole calculation uses, and this page explains where it comes from.
This is the foundation for two Class 11 Chemistry chapters examined in both JEE Main and NEET.
Some Basic Concepts of Chemistry builds the mole concept on average atomic masses. Molar mass, stoichiometry and every calculation of how much reacts with how much use the periodic table's non-whole numbers directly, and the Class 9 understanding that those numbers are weighted averages over isotopes is what stops them looking arbitrary. That chapter also treats the laws of chemical combination whose failure on Dalton's second postulate this page explains.
Structure of Atom takes the electronic configuration much further. The Bohr-Bury shells become subshells — s, p, d and f — filled by the Aufbau principle, with Hund's rule and the Pauli exclusion principle added. The Class 9 anomaly worked above, that potassium is rather than , is explained there by the 4s subshell filling before the 3d — so the rule learned here as an instruction is justified there as a consequence.
Where valency is reused. Class 11 Classification of Elements and Periodicity explains group behaviour by the number of valence electrons, and Class 11 Chemical Bonding turns the losing, gaining and sharing described on this page into ionic and covalent bonds. The reason carbon shares rather than transfers, given above, becomes the whole of Class 11 and Class 12 organic chemistry.
Isotopes feed into Class 12 Physics Nuclei and into radiochemistry, where the applications named here are treated quantitatively with half-lives.
What the questions look like. Numericals on average atomic mass are common, and the harder version is the backwards one — given the average, find the abundances — which is worked example 5 above. Match-the-column items pair an element with its configuration or its valency. Assertion-reason questions favour two statements from this page: that isotopes have identical chemical properties, and that a shell's capacity is while the outermost is capped at . Classification questions give two species with their numbers and ask for isotopes or isobars, which is a one-step comparison of the bottom numbers.
How board and competitive emphasis differ. A board paper asks you to write configurations up to , define isotopes and isobars with two examples each, and compute one average atomic mass forwards. A competitive paper sets the reverse calculation, or asks which of four given configurations is impossible — which tests the outermost-shell cap rather than the ability to fill shells in order.
The single trap that costs the most marks. Writing potassium as ****. The M shell can hold in general, but not while it is the outermost shell, where the limit is . This one configuration accounts for a remarkable share of the marks lost on this topic, and it is worth writing potassium and calcium out by hand until they come automatically.
A second trap worth naming. Confusing isotopes with isobars because both words are unfamiliar. Fix them by their meaning: isotope keeps the element the same, so the atomic number is what matches; isobar keeps the mass the same. Compare the bottom numbers first and the classification takes one second.
This is the foundation for two Class 11 Chemistry chapters examined in both JEE Main and NEET.
Some Basic Concepts of Chemistry builds the mole concept on average atomic masses. Molar mass, stoichiometry and every calculation of how much reacts with how much use the periodic table's non-whole numbers directly, and the Class 9 understanding that those numbers are weighted averages over isotopes is what stops them looking arbitrary. That chapter also treats the laws of chemical combination whose failure on Dalton's second postulate this page explains.
Structure of Atom takes the electronic configuration much further. The Bohr-Bury shells become subshells — s, p, d and f — filled by the Aufbau principle, with Hund's rule and the Pauli exclusion principle added. The Class 9 anomaly worked above, that potassium is rather than , is explained there by the 4s subshell filling before the 3d — so the rule learned here as an instruction is justified there as a consequence.
Where valency is reused. Class 11 Classification of Elements and Periodicity explains group behaviour by the number of valence electrons, and Class 11 Chemical Bonding turns the losing, gaining and sharing described on this page into ionic and covalent bonds. The reason carbon shares rather than transfers, given above, becomes the whole of Class 11 and Class 12 organic chemistry.
Isotopes feed into Class 12 Physics Nuclei and into radiochemistry, where the applications named here are treated quantitatively with half-lives.
What the questions look like. Numericals on average atomic mass are common, and the harder version is the backwards one — given the average, find the abundances — which is worked example 5 above. Match-the-column items pair an element with its configuration or its valency. Assertion-reason questions favour two statements from this page: that isotopes have identical chemical properties, and that a shell's capacity is while the outermost is capped at . Classification questions give two species with their numbers and ask for isotopes or isobars, which is a one-step comparison of the bottom numbers.
How board and competitive emphasis differ. A board paper asks you to write configurations up to , define isotopes and isobars with two examples each, and compute one average atomic mass forwards. A competitive paper sets the reverse calculation, or asks which of four given configurations is impossible — which tests the outermost-shell cap rather than the ability to fill shells in order.
The single trap that costs the most marks. Writing potassium as ****. The M shell can hold in general, but not while it is the outermost shell, where the limit is . This one configuration accounts for a remarkable share of the marks lost on this topic, and it is worth writing potassium and calcium out by hand until they come automatically.
A second trap worth naming. Confusing isotopes with isobars because both words are unfamiliar. Fix them by their meaning: isotope keeps the element the same, so the atomic number is what matches; isobar keeps the mass the same. Compare the bottom numbers first and the classification takes one second.
Key takeaways
Configurations, valency, isotopes and atomic mass: quick revision
- **Shell capacity is **: K , L , M , N — but the **outermost shell never holds more than **, and that rule takes priority.
- Configurations: Na () ; Al () ; S () ; Cl () ; Ar () .
- **Potassium () is and calcium () is ** — never or .
- Shells are filled stepwise from the innermost outward.
- Valency: if valence electrons are or fewer, valency equals them; if more than , valency is minus them.
- So Na , Mg , Al , C , N , O , Cl , and **noble gases — which is why they are inert.
- Valency depends on the outermost shell only**, so sodium and potassium both have valency .
- Valencies give formulas: from and , from and .
- Carbon, with exactly valence electrons, shares rather than transferring — the basis of organic chemistry.
- Isotopes: same , different . Hydrogen's protium, deuterium and tritium; and ; and .
- Isobars: different , same . with , and with .
- Classify by the bottom number: same means isotopes, different with equal means isobars.
- Isotopes have identical chemical and different physical properties, so they cannot be separated chemically.
- Average atomic mass .
- Chlorine: u. Carbon: u. Boron: u. Neon: u.
- Backwards: isotopes of and averaging u means of the lighter one.
- The average lies between the two mass numbers, nearer the commoner isotope.
- Applications: uranium as reactor fuel, cobalt for cancer treatment, iodine for goitre.
- u describes no single atom — it describes the sample, which is what a chemist actually weighs.
Write the configurations of all twenty elements from memory and mark the two where the outermost-shell rule overrules — if you spot both, this topic will not catch you out.
- Configurations: Na () ; Al () ; S () ; Cl () ; Ar () .
- **Potassium () is and calcium () is ** — never or .
- Shells are filled stepwise from the innermost outward.
- Valency: if valence electrons are or fewer, valency equals them; if more than , valency is minus them.
- So Na , Mg , Al , C , N , O , Cl , and **noble gases — which is why they are inert.
- Valency depends on the outermost shell only**, so sodium and potassium both have valency .
- Valencies give formulas: from and , from and .
- Carbon, with exactly valence electrons, shares rather than transferring — the basis of organic chemistry.
- Isotopes: same , different . Hydrogen's protium, deuterium and tritium; and ; and .
- Isobars: different , same . with , and with .
- Classify by the bottom number: same means isotopes, different with equal means isobars.
- Isotopes have identical chemical and different physical properties, so they cannot be separated chemically.
- Average atomic mass .
- Chlorine: u. Carbon: u. Boron: u. Neon: u.
- Backwards: isotopes of and averaging u means of the lighter one.
- The average lies between the two mass numbers, nearer the commoner isotope.
- Applications: uranium as reactor fuel, cobalt for cancer treatment, iodine for goitre.
- u describes no single atom — it describes the sample, which is what a chemist actually weighs.
Write the configurations of all twenty elements from memory and mark the two where the outermost-shell rule overrules — if you spot both, this topic will not catch you out.