Why is the atomic mass on the periodic table a decimal if mass numbers are whole numbers?

The periodic table lists the weighted average atomic mass of all naturally occurring isotopes of that element, weighted by how abundant each one is. Chlorine's value near 35.45 reflects a mixture that is roughly three-quarters chlorine-35 and one-quarter chlorine-37. No individual chlorine atom has that mass. When a question asks for the neutrons in a specific isotope, use that isotope's whole-number mass number, not the table's average.

Does an ion's charge change its mass number?

No. Mass number counts only protons and neutrons, and forming an ion only moves electrons. An electron has about 1/1836 the mass of a proton, so gaining or losing a few electrons changes the actual mass by a negligible amount and changes the mass number not at all. That is why ^23Na and ^23Na^+ carry the same superscript 23.

Can two different elements have the same mass number?

Yes, and it happens often. Argon-40 and calcium-40 both have A = 40, but argon has 18 protons and 22 neutrons while calcium has 20 protons and 20 neutrons. Species like these are called isobars. Since Z differs, they are entirely different elements with different chemistry — another reminder that the proton count, not the mass number, sets identity.

How do I tell whether to add or subtract electrons for an ion?

Use electrons = Z - charge and let the sign do the work. A charge of +2 gives Z - 2 (electrons were lost), and a charge of -2 gives Z + 2 (electrons were gained). Check your answer by asking whether it makes the species come out with the charge you were given: more electrons than protons must mean negative.

CHEM-2.2

Subatomic Particles & Isotope Notation

Learn to read isotope notation and count protons, neutrons, and electrons in atoms and ions — plus why isotopes of an element behave the same chemically.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on Subatomic Particles & Isotope Notation, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start Subatomic Particles & Isotope Notation free

What this lesson covers

An atom's identity is decided by one number: how many protons sit in its nucleus. Everything else — how heavy it is, whether it carries a charge, whether it is radioactive — is written around that number. Isotope notation is chemistry's compact way of packing all of that information into a single symbol, and once you can read it, you can pull out the exact count of protons, neutrons, and electrons in a few seconds.

In this lesson you will learn what each subatomic particle contributes to mass and charge, how the symbols

^{A}_{Z}\text{X}

and element-mass hyphen notation encode that information, how to adjust electron counts for monatomic ions, and why carbon-12 and carbon-14 form the same bonds and appear in the same place on the periodic table even though one is radioactive and the other is not.

The Three Particles: Mass, Charge, and Location

An atom is built from three particles, and each one has a distinct job. Protons and neutrons are packed into the tiny, dense nucleus; electrons occupy the enormous volume of space around it.

Particle	Charge	Relative mass	Location
Proton	$+1$	$\approx 1$ amu	Nucleus
Neutron	$0$	$\approx 1$ amu	Nucleus
Electron	$-1$	$\approx \frac{1}{1836}$ amu	Outside nucleus

Two consequences follow immediately. First, essentially all of an atom's mass comes from the nucleus, because an electron weighs less than a two-thousandth of a proton. That is why the mass number counts only protons and neutrons. Second, essentially all of an atom's volume is empty space occupied by electrons, and that outer electron region is what other atoms actually touch during a reaction.

The atomic number

Z

equals the number of protons and is the element's fingerprint. Change

Z

and you have a different element — that is nuclear chemistry, not a chemical reaction. Change the neutron count and you have a different isotope of the same element. Change the electron count and you have an ion of the same element.

A frequent misconception is that the number of electrons defines the element. It does not. A sodium ion,

\text{Na}^{+}

, has ten electrons, exactly like a neon atom, but it is still sodium because it still has 11 protons. Neutral atoms happen to have electrons equal to protons, which makes it easy to blur the two ideas, so build the habit now of always reading the element from

Z

Reading Isotope Notation

The standard nuclide symbol places two numbers on the left of the element symbol:

^{A}_{Z}\text{X}

Here

Z

is the atomic number (protons) on the bottom and

A

is the mass number (protons plus neutrons) on the top. So for

^{31}_{15}\text{P}

, there are 15 protons and

31 - 15 = 16

neutrons.

The neutron formula is worth memorizing as a rearrangement rather than a separate fact:

A = Z + N \quad\Longrightarrow\quad N = A - Z

Because

Z

is already determined by the element symbol, the subscript is technically redundant, and many textbooks drop it. That gives hyphen notation: carbon-14 means the carbon isotope with

A = 14

, so

Z = 6

from the periodic table and

N = 14 - 6 = 8

.

The single most common error here is treating the decimal number printed on the periodic table as the mass number. Chlorine's tile reads about

35.45

, but no chlorine atom has a mass number of 35.45. That value is the weighted average atomic mass of the naturally occurring mixture. Mass numbers are always whole numbers because you cannot have a fraction of a nucleon. If a question hands you a periodic table value and asks for neutrons in a specific isotope, you need the isotope's own mass number, not the average.

A second error is reversing the positions of

A

and

Z

. A quick sanity check: the top number must be larger than or equal to the bottom number, and for every element except hydrogen-1 it is strictly larger. If your top number is smaller, you have flipped them.

Counting Electrons in Ions

Protons and neutrons never change when an atom becomes an ion — chemistry happens in the electron cloud. So the recipe splits cleanly:

\text{protons} = Z, \qquad \text{neutrons} = A - Z, \qquad \text{electrons} = Z - (\text{charge})

Subtracting the charge feels backwards until you see why. A charge of

+2

means the atom has two more positive units than negative units, so it lost two electrons:

Z - (+2) = Z - 2

. A charge of

-1

means one extra electron:

Z - (-1) = Z + 1

. Cations (positive) have fewer electrons than protons; anions (negative) have more.

Species	Protons	Neutrons	Electrons
$^{39}_{19}\text{K}$	19	20	19
$^{39}_{19}\text{K}^{+}$	19	20	18
$^{32}_{16}\text{S}^{2-}$	16	16	18
$^{27}_{13}\text{Al}^{3+}$	13	14	10

Notice that

\text{K}^{+}

and

\text{S}^{2-}

both have 18 electrons. Species with matching electron counts are called isoelectronic, and they are still completely different substances because their nuclei differ.

Where students go wrong: adding electrons for a positive charge. Anchor the logic on a real case — sodium metal reacts by giving away one electron, and the result is written

\text{Na}^{+}

. Losing a negative particle leaves a net positive. Also remember that the charge superscript never touches the mass number; removing electrons changes an ion's mass by a truly negligible amount, so

^{23}\text{Na}

and

^{23}\text{Na}^{+}

share the same mass number.

Why Isotopes Behave Alike Chemically

Chemical behavior is electron behavior. Bonds form when valence electrons are shared, transferred, or rearranged, and the number and arrangement of those electrons is set by the nuclear charge,

Z

. Neutrons carry no charge, so adding or removing them does not change how strongly the nucleus attracts electrons and does not change how many electrons a neutral atom holds.

That is the whole argument. Carbon-12, carbon-13, and carbon-14 each have 6 protons, so each neutral atom has 6 electrons arranged identically, with 4 valence electrons. All three form four bonds, all three make carbon dioxide when burned, all three are metabolized by plants. This is precisely why radiocarbon dating works: living things absorb carbon-14 in the same reactions that absorb carbon-12, because the organism's enzymes cannot chemically tell them apart.

What isotopes do differ in is mass and nuclear stability. Heavier isotopes diffuse slightly more slowly and react at slightly different rates — a measurable effect called the kinetic isotope effect, most noticeable for hydrogen versus deuterium where the mass literally doubles. Some isotopes have unstable nuclei and undergo radioactive decay. Neither of these is a difference in chemical bonding preference.

A misconception worth naming: students sometimes say isotopes are different elements or that they occupy different periodic table positions. They do not. The periodic table is organized by

Z

, so every isotope of chlorine sits in the same box. A related slip is claiming isotopes have different charges. Neutral isotopes are all neutral; neutron count has nothing to do with charge. Keep the three variables separate — protons set identity, neutrons set mass and stability, electrons set charge and chemistry.

Key terms

Atomic number ( $Z$ ).: The number of protons in an atom's nucleus. It defines which element the atom is and equals the electron count in a neutral atom.
Mass number ( $A$ ).: The total count of protons plus neutrons in a nucleus. Always a whole number, and specific to one isotope.
Isotope.: Atoms of the same element (same $Z$ ) that have different numbers of neutrons, and therefore different mass numbers.
Nuclide symbol.: The notation $^{A}_{Z}\text{X}$ , with mass number written as a superscript and atomic number as a subscript before the element symbol.
Monatomic ion.: A single atom that has gained or lost electrons, giving it a net negative or positive charge while its proton count stays fixed.
Cation.: A positively charged ion formed when an atom loses one or more electrons, so electrons are fewer than protons.
Anion.: A negatively charged ion formed when an atom gains one or more electrons, so electrons outnumber protons.
Isoelectronic.: Describing two or more different species that contain the same number of electrons, such as $\text{Na}^{+}$ , $\text{F}^{-}$ , and neon.

Worked example

An iron ion is written as

^{56}_{26}\text{Fe}^{3+}

. Determine the number of protons, neutrons, and electrons, and state whether this species has the same chemical behavior as

^{54}_{26}\text{Fe}

Start with protons, which come straight from the subscript:

Z = 26

, so there are 26 protons. This is what makes it iron, and it will not change no matter what the charge is.

Next, neutrons. Use

N = A - Z

. The mass number is the superscript,

A = 56

, so

N = 56 - 26 = 30

. There are 30 neutrons. Notice the charge played no role here — the superscript charge sits after the symbol and never enters the mass calculation.

Now electrons. Apply

\text{electrons} = Z - \text{charge} = 26 - (+3) = 23

. There are 23 electrons. Check the logic: a

3+

charge means three more protons than electrons, and

26 - 23 = 3

. That confirms the sign is right. If you had gotten 29, you would have added electrons to make something positive, which is backwards.

Finally, the comparison. The species

^{54}_{26}\text{Fe}

also has 26 protons, so it is the same element, just a different isotope with

54 - 26 = 28

neutrons. As neutral atoms, iron-54 and iron-56 have identical electron counts and identical valence arrangements, so they show the same chemical behavior — both rust, both form

\text{Fe}^{2+}

and

\text{Fe}^{3+}

ions. However, the species in the problem,

^{56}_{26}\text{Fe}^{3+}

, is an ion, not a neutral atom. It has already lost three electrons, so its reactivity differs from that of a neutral iron atom. The correct statement is that neutral iron-54 and neutral iron-56 behave identically; the difference between

^{56}\text{Fe}^{3+}

and

^{54}\text{Fe}

is a charge difference, not an isotope effect.

Practice questions

How many protons, neutrons, and electrons are in the ion

^{80}_{35}\text{Br}^{-}

35 protons, 45 neutrons, 34 electrons
35 protons, 45 neutrons, 36 electrons
35 protons, 80 neutrons, 36 electrons
45 protons, 35 neutrons, 35 electrons

Answer: 35 protons, 45 neutrons, 36 electrons

Protons come from the subscript:

Z = 35

. Neutrons come from

N = A - Z = 80 - 35 = 45

; the mass number 80 is protons plus neutrons, not neutrons alone, which rules out the option listing 80 neutrons. For electrons, a

1-

charge means the atom gained one electron, so

35 - (-1) = 36

. The option with 34 electrons comes from subtracting instead of adding, the mistake students make most often with anions.

Magnesium-25 and magnesium-26 are both stable isotopes found in nature. Explain why a chemist cannot separate them by running an ordinary chemical reaction, and identify one measurable property that does differ between them.

Answer: Both isotopes have 12 protons and, as neutral atoms, 12 electrons arranged identically with 2 valence electrons, so they undergo exactly the same chemical reactions; they differ in mass (25 amu versus 26 amu, from 13 versus 14 neutrons).

Chemical reactions are governed by valence electrons and the nuclear charge that holds them. Since both isotopes have

Z = 12

, their electron structures are indistinguishable, so both react with oxygen to form MgO and both lose two electrons to form

\text{Mg}^{2+}

. Neutrons are uncharged and do not affect this. What does differ is mass: magnesium-26 has one extra neutron, so it is measurably heavier. That mass difference is what a mass spectrometer exploits to separate and count isotopes, and it can produce very slight differences in diffusion and reaction rates — but not a difference in which products form.

A neutral atom of an element contains 34 electrons and 45 neutrons. Write its complete nuclide symbol.

Answer: $^{79}_{34}\text{Se}$

Because the atom is neutral, electrons equal protons, so

Z = 34

. Element 34 on the periodic table is selenium, symbol Se. The mass number is protons plus neutrons:

A = 34 + 45 = 79

. Assembling the symbol with

A

on top and

Z

on the bottom gives

^{79}_{34}\text{Se}

. Students sometimes write 45 as the superscript by treating the neutron count as the mass number; remember that

A

always includes the protons too.

FAQ

Why is the atomic mass on the periodic table a decimal if mass numbers are whole numbers?: The periodic table lists the weighted average atomic mass of all naturally occurring isotopes of that element, weighted by how abundant each one is. Chlorine's value near 35.45 reflects a mixture that is roughly three-quarters chlorine-35 and one-quarter chlorine-37. No individual chlorine atom has that mass. When a question asks for the neutrons in a specific isotope, use that isotope's whole-number mass number, not the table's average.
Does an ion's charge change its mass number?: No. Mass number counts only protons and neutrons, and forming an ion only moves electrons. An electron has about $1/1836$ the mass of a proton, so gaining or losing a few electrons changes the actual mass by a negligible amount and changes the mass number not at all. That is why $^{23}\text{Na}$ and $^{23}\text{Na}^{+}$ carry the same superscript 23.
Can two different elements have the same mass number?: Yes, and it happens often. Argon-40 and calcium-40 both have $A = 40$ , but argon has 18 protons and 22 neutrons while calcium has 20 protons and 20 neutrons. Species like these are called isobars. Since $Z$ differs, they are entirely different elements with different chemistry — another reminder that the proton count, not the mass number, sets identity.
How do I tell whether to add or subtract electrons for an ion?: Use $\text{electrons} = Z - \text{charge}$ and let the sign do the work. A charge of $+2$ gives $Z - 2$ (electrons were lost), and a charge of $-2$ gives $Z + 2$ (electrons were gained). Check your answer by asking whether it makes the species come out with the charge you were given: more electrons than protons must mean negative.

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