Particles in the Atom and Isotopes

AS · 12 min

Every explanation in chemistry eventually comes back to three particles: protons, neutrons and electrons, and where they sit in the atom. This note sets out what those particles are, how they behave in an electric field, how to count them in atoms and ions, why atomic and ionic radii change across the Periodic Table, and what isotopes are. These ideas are tested directly in Paper 1 and Paper 2 short-answer questions, and they underpin ionisation energy, bonding and mass spectrometry.

The nuclear atom

An atom is almost entirely empty space. At its centre is a tiny, very dense nucleus that contains the protons and neutrons. The electrons are found in shells (energy levels) in the space around the nucleus.

The scale is extreme. A typical atom has a radius of about $10^{-10}\ \text{m}$ , while its nucleus has a radius of about $10^{-15}\ \text{m}$ . If the nucleus were a marble in the centre of a football stadium, the electrons would be specks moving around the outer stands. Yet the nucleus contains more than 99.9% of the mass of the atom.

Key result

Almost all of the mass of an atom is in the nucleus (protons and neutrons).
All of the positive charge is in the nucleus (protons).
The negative charge is spread through the much larger volume around the nucleus (electrons).
An atom is neutral because the number of electrons equals the number of protons.

The three subatomic particles

particle	relative charge	relative mass	location
proton	$+1$	$1$	nucleus
neutron	$0$	$1$	nucleus
electron	$-1$	$\tfrac{1}{1836}$ (about $0.0005$ )	shells around the nucleus

Relative values are used because the real values are tiny and awkward. The actual charge on a proton is $+1.60 \times 10^{-19}\ \text{C}$ and its mass is $1.67 \times 10^{-27}\ \text{kg}$ ; you are never asked to recall these.

Watch out

The relative mass of an electron is not zero. It is $\tfrac{1}{1836}$ , which is negligible when you add up the mass of an atom but matters when you compare how particles are deflected in an electric field. Write $\tfrac{1}{1836}$ or "negligible", never "0".

Proton number and nucleon number

Definition

The proton number (also called the atomic number), $Z$ , is the number of protons in the nucleus of an atom.

The nucleon number (also called the mass number), $A$ , is the total number of protons and neutrons in the nucleus of an atom.

The proton number defines the element. Every atom with 17 protons is chlorine; change the number of protons and you have a different element. The number of neutrons is $A - Z$ .

Nuclides are written with the nucleon number at the top left and the proton number at the bottom left of the symbol:

\ce{^{A}_{Z}X} \qquad \text{for example} \qquad \ce{^{35}_{17}Cl}\ \text{has 17 protons and } 35 - 17 = 18 \text{ neutrons.}

Counting particles in atoms and ions

An ion forms when an atom gains or loses electrons. The nucleus is unchanged, so the numbers of protons and neutrons are the same as in the atom.

Method

Protons $= Z$ (from the Periodic Table or the subscript).
Neutrons $= A - Z$ .
Electrons $= Z - (\text{charge})$ . A $2+$ ion has two fewer electrons than protons; a $3-$ ion has three more.

Counting particles in ions

Complete the table for $\ce{^{24}_{12}Mg^2+}$ , $\ce{^{32}_{16}S^2-}$ and $\ce{^{56}_{26}Fe^3+}$ .

Solution

species	protons	neutrons	electrons
$\ce{^{24}_{12}Mg^2+}$	12	$24 - 12 = 12$	$12 - 2 = 10$
$\ce{^{32}_{16}S^2-}$	16	$32 - 16 = 16$	$16 + 2 = 18$
$\ce{^{56}_{26}Fe^3+}$	26	$56 - 26 = 30$	$26 - 3 = 23$

A negative charge means extra electrons, so electrons $= Z + 2$ for $\ce{S^2-}$ .

Identifying a species from its particles

A species contains 20 protons, 22 neutrons and 18 electrons. Write its full symbol.

Solution

Twenty protons means the element is calcium, $Z = 20$ . Nucleon number $= 20 + 22 = 42$ . Charge $= 20 - 18 = +2$ .

\ce{^{42}_{20}Ca^2+}

Beams of particles in an electric field

If beams of protons, neutrons and electrons, all moving at the same velocity, pass between two charged plates, each particle is affected according to its charge and its mass.

Charge decides the direction. Positive particles are attracted towards the negative plate; negative particles towards the positive plate; neutral particles are not deflected at all.
Mass decides how far. For the same charge and speed, a lighter particle is deflected more because it has less inertia.

The angle of deflection is proportional to the charge-to-mass ratio:

Key result

\text{angle of deflection} \propto \frac{\text{charge}}{\text{mass}}

Beams of particles at the same speed between charged plates. Neutrons pass straight through. Protons bend slightly towards the negative plate. Electrons bend sharply towards the positive plate, because their charge-to-mass ratio is about 1836 times larger.

For a proton the ratio is $\tfrac{+1}{1} = +1$ ; for an electron it is $\tfrac{-1}{1/1836} = -1836$ . So electrons are deflected in the opposite direction and through a much larger angle than protons. For ions the same rule applies: compare charge divided by mass.

Comparing deflections of ions

Beams of $\ce{^{1}H+}$ , $\ce{^{2}H+}$ and $\ce{^{4}He^2+}$ ions travel at the same speed into the same electric field. Compare their deflections.

Solution

All three are positive, so all are deflected towards the negative plate.

ion	charge	mass	charge/mass
$\ce{^{1}H+}$	$+1$	$1$	$1$
$\ce{^{2}H+}$	$+1$	$2$	$0.5$
$\ce{^{4}He^2+}$	$+2$	$4$	$0.5$

$\ce{^{1}H+}$ is deflected most. $\ce{^{2}H+}$ and $\ce{^{4}He^2+}$ have the same charge-to-mass ratio, so they are deflected through the same angle, half that of $\ce{^{1}H+}$ .

Exam tip

"Describe the behaviour of beams of protons, neutrons and electrons in an electric field" is a three-mark question. One mark each for: neutrons undeflected (no charge); protons deflected towards the negative plate; electrons deflected towards the positive plate by a larger angle (because they are much lighter). Always give the direction and the relative size.

Atomic radius and ionic radius

Atomic radius depends on a balance between two things: the attraction of the nucleus for the outer electrons, and the number of shells holding those electrons out.

Three factors control that balance. You will meet them again in ionisation energy and electronegativity, so learn them now.

Nuclear charge: the number of protons. More protons pull the electrons in more strongly.
Number of shells: each extra shell puts the outer electrons further from the nucleus.
Shielding: inner shells of electrons repel the outer electrons and reduce the pull they feel from the nucleus.

Across a period: atomic radius decreases

Going from sodium to chlorine, the nuclear charge increases by one each step. The extra electron goes into the same outer shell, so the number of shells and the shielding by inner shells stay roughly the same. The greater nuclear charge pulls the outer shell closer, so the atomic radius decreases.

Down a group: atomic radius increases

Going down Group 1 from lithium to caesium, each element has one more shell of electrons. The outer electrons are further from the nucleus and more shielded by inner shells. Although the nuclear charge increases, the extra shell outweighs it, so the atomic radius increases.

Ions compared with atoms

A cation is smaller than its atom. A metal atom such as $\ce{Na}$ ( $2,8,1$ ) loses its outer shell to form $\ce{Na+}$ ( $2,8$ ). There is one fewer shell, and now more protons than electrons, so each electron is pulled in more strongly.
An anion is larger than its atom. A non-metal atom such as $\ce{Cl}$ gains an electron to form $\ce{Cl-}$ . The nuclear charge is unchanged but there are more electrons in the outer shell, so there is more repulsion between electrons and the same nuclear charge is shared among more electrons.

Ionic radius across Period 3

species	$\ce{Na+}$	$\ce{Mg^2+}$	$\ce{Al^3+}$	$\ce{Si^4+}$	$\ce{P^3-}$	$\ce{S^2-}$	$\ce{Cl-}$
electrons	10	10	10	10	18	18	18
radius / nm	0.095	0.065	0.050	0.041	0.212	0.184	0.181

Two patterns explain this table.

$\ce{Na+}$ to $\ce{Si^4+}$ are isoelectronic (same number of electrons, $2,8$ ). The nuclear charge rises from 11 to 14, so the same electrons are pulled in more tightly and the radius falls.
$\ce{P^3-}$ to $\ce{Cl-}$ are also isoelectronic with each other ( $2,8,8$ ). They have one more shell than the cations, so there is a big jump in radius between $\ce{Si^4+}$ and $\ce{P^3-}$ . Across the anions the nuclear charge rises from 15 to 17, so the radius falls again.

Key result

Across a period: atomic radius decreases (nuclear charge up, same shell, similar shielding).
Down a group: atomic radius increases (extra shell, more shielding).
Cations are smaller than their atoms; anions are larger.
In an isoelectronic series, the species with the most protons is the smallest.

Ordering an isoelectronic series

Put $\ce{O^2-}$ , $\ce{F-}$ , $\ce{Na+}$ and $\ce{Mg^2+}$ in order of increasing radius, and explain.

Solution

All four have 10 electrons ( $1s^2 2s^2 2p^6$ ), so they are isoelectronic. Their nuclear charges are $8, 9, 11, 12$ . The greater the nuclear charge, the more strongly the same 10 electrons are attracted, so the smaller the ion.

\ce{Mg^2+} < \ce{Na+} < \ce{F-} < \ce{O^2-}

Watch out

Do not say an atom gets smaller across a period "because it has more electrons". More electrons on their own would make it bigger. The decrease is because the nuclear charge increases while the electrons are added to the same shell with similar shielding.

Isotopes

Definition

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

Chlorine has two common isotopes, $\ce{^{35}_{17}Cl}$ (17 protons, 18 neutrons) and $\ce{^{37}_{17}Cl}$ (17 protons, 20 neutrons). Hydrogen has three: $\ce{^{1}_{1}H}$ , $\ce{^{2}_{1}H}$ (deuterium) and $\ce{^{3}_{1}H}$ (tritium).

Same chemical properties

Chemical reactions involve electrons, and specifically the outer electrons. Isotopes of an element have the same number of protons and therefore the same number and arrangement of electrons. So they react in exactly the same way: $\ce{^{35}Cl2}$ and $\ce{^{37}Cl2}$ both react with sodium to make sodium chloride.

Different physical properties

Isotopes have different numbers of neutrons, so their atoms have different masses. Physical properties that depend on mass therefore differ. The syllabus limits this to mass and density. For example, "heavy water", $\ce{D2O}$ (made with deuterium), has a density of about $1.11\ \text{g cm}^{-3}$ compared with $1.00\ \text{g cm}^{-3}$ for ordinary water, because each molecule is heavier but about the same size.

Exam tip

For "explain why isotopes have the same chemical properties" you need two linked points: same number of electrons (or same electronic configuration) and chemical properties depend on electrons. "Same number of protons" on its own does not earn the mark. For physical properties: "different number of neutrons so different mass, therefore different density".

Neutrons and electrons in a set of species

Consider these four species:

\ce{^{40}_{18}Ar} \qquad \ce{^{39}_{19}K+} \qquad \ce{^{40}_{20}Ca} \qquad \ce{^{37}_{17}Cl-}

(a) Which species have the same number of neutrons? (b) Which species have the same number of electrons?

Solution

(a) Neutrons $= A - Z$ : argon $40 - 18 = 22$ ; potassium $39 - 19 = 20$ ; calcium $40 - 20 = 20$ ; chlorine $37 - 17 = 20$ . So $\ce{^{39}K+}$ , $\ce{^{40}Ca}$ and $\ce{^{37}Cl-}$ each have 20 neutrons.

(b) Electrons: argon 18; $\ce{K+}$ $19 - 1 = 18$ ; calcium 20; $\ce{Cl-}$ $17 + 1 = 18$ . So $\ce{Ar}$ , $\ce{K+}$ and $\ce{Cl-}$ are isoelectronic, with 18 electrons each.

Count every species before choosing: questions like this are designed so that a quick guess picks the wrong set.

Exam-style: deflection and identity

A beam of particles X, each with 11 protons, 12 neutrons and 10 electrons, is passed through an electric field alongside a beam of protons travelling at the same speed.

(a) Identify X. (b) State and explain how the deflection of X compares with that of the protons.

Solution

(a) 11 protons means sodium. Mass number $= 11 + 12 = 23$ . Charge $= 11 - 10 = +1$ . X is $\ce{^{23}_{11}Na+}$ .

(b) X is positive, so it is deflected towards the negative plate, the same direction as the protons. Its charge-to-mass ratio is $\tfrac{1}{23}$ compared with $\tfrac{1}{1}$ for a proton, so X is deflected through a much smaller angle (about one twenty-third of the proton's deflection), because it has the same charge but 23 times the mass.

Summary

The atom is mostly empty space with a tiny, dense, positive nucleus of protons and neutrons; electrons occupy shells around it.
Relative charges: proton $+1$ , neutron $0$ , electron $-1$ . Relative masses: $1$ , $1$ , $\tfrac{1}{1836}$ .
Proton (atomic) number $Z$ = protons; nucleon (mass) number $A$ = protons + neutrons; neutrons $= A - Z$ ; electrons $= Z -$ charge.
In an electric field, deflection $\propto$ charge/mass: neutrons straight, protons slightly to $(-)$ , electrons strongly to $(+)$ .
Atomic radius decreases across a period (nuclear charge increases, same shell) and increases down a group (extra shells).
Cations are smaller than their atoms; anions are larger. In an isoelectronic series, more protons means smaller.
Isotopes: same protons, different neutrons. Same chemical properties (same electrons), different mass and density.

Practice

Question

State the relative charge and relative mass of a neutron and of an electron.
Give the numbers of protons, neutrons and electrons in $\ce{^{27}_{13}Al^3+}$ and in $\ce{^{79}_{35}Br-}$ .
A species has 16 protons, 18 neutrons and 18 electrons. Write its symbol with nucleon number, proton number and charge.
Explain why the atomic radius of magnesium is smaller than that of sodium.
Explain why the radius of a $\ce{Cl-}$ ion is larger than the radius of a chlorine atom.
Arrange $\ce{S^2-}$ , $\ce{Cl-}$ , $\ce{K+}$ and $\ce{Ca^2+}$ in order of decreasing radius. Explain your order.
Explain why $\ce{^{35}Cl}$ and $\ce{^{37}Cl}$ have the same chemical properties but different densities as gases.
Beams of $\ce{^{3}H+}$ , $\ce{^{3}He^2+}$ and $\ce{^{4}He+}$ enter the same electric field at the same speed. Rank them by angle of deflection, largest first.
Explain the large increase in ionic radius from $\ce{Si^4+}$ (0.041 nm) to $\ce{P^3-}$ (0.212 nm), and why the radius then decreases from $\ce{P^3-}$ to $\ce{Cl-}$ .
A student says: "Down Group 2 the nuclear charge increases, so the atoms should get smaller." Explain why the student is wrong.

Answers

Neutron: charge $0$ , mass $1$ . Electron: charge $-1$ , mass $\tfrac{1}{1836}$ (negligible).
$\ce{^{27}_{13}Al^3+}$ : 13 protons, $27 - 13 = 14$ neutrons, $13 - 3 = 10$ electrons. $\ce{^{79}_{35}Br-}$ : 35 protons, $79 - 35 = 44$ neutrons, $35 + 1 = 36$ electrons.
16 protons is sulfur; $A = 16 + 18 = 34$ ; charge $= 16 - 18 = -2$ . Symbol $\ce{^{34}_{16}S^2-}$ .
Magnesium has one more proton (greater nuclear charge, 12 compared with 11). Its outer electrons are in the same shell (third shell) with the same inner-shell shielding, so they are attracted more strongly and pulled closer to the nucleus.
$\ce{Cl-}$ has one more electron than the atom but the same nuclear charge (17 protons). The extra electron increases repulsion between the outer electrons, and the same nuclear charge is attracting 18 electrons instead of 17, so the electron cloud expands.
All four have 18 electrons (isoelectronic). Nuclear charges: S 16, Cl 17, K 19, Ca 20. More protons attract the same electrons more strongly, so: $\ce{S^2-} > \ce{Cl-} > \ce{K+} > \ce{Ca^2+}$ .
Both isotopes have 17 protons and 17 electrons, with the same electronic configuration; chemical reactions depend on electrons, so the reactions are identical. They have different numbers of neutrons (18 and 20), so different atomic masses; a gas sample of the heavier isotope has a greater mass in the same volume, so a greater density.
Charge/mass: $\ce{^{3}H+} = \tfrac{1}{3} \approx 0.33$ ; $\ce{^{3}He^2+} = \tfrac{2}{3} \approx 0.67$ ; $\ce{^{4}He+} = \tfrac{1}{4} = 0.25$ . All deflect towards the negative plate. Order of deflection: $\ce{^{3}He^2+} > \ce{^{3}H+} > \ce{^{4}He+}$ .
$\ce{Si^4+}$ has the configuration $2,8$ (two shells); $\ce{P^3-}$ has $2,8,8$ (three shells). The extra occupied shell makes $\ce{P^3-}$ much larger. $\ce{P^3-}$ , $\ce{S^2-}$ and $\ce{Cl-}$ all have 18 electrons, but the nuclear charge increases (15, 16, 17), so the same electrons are attracted more strongly and the radius decreases.
Each element down the group has an extra shell of electrons. The outer electrons are further from the nucleus and more shielded by the extra inner shells. This effect outweighs the increase in nuclear charge, so atomic radius increases down the group.

The nuclear atom

The three subatomic particles

Proton number and nucleon number

Counting particles in atoms and ions

Beams of particles in an electric field

Atomic radius and ionic radius

Across a period: atomic radius decreases

Down a group: atomic radius increases

Ions compared with atoms

Ionic radius across Period 3

Isotopes

Same chemical properties

Different physical properties

Practice

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