Skip to content

Course home

Sign up

1.1 The particle model

1.1.1 Development of the atomic model

Scientific models of the atom

Definition

Scientific model

A simplified representation of something that cannot be observed directly, used to explain observations and to make predictions that can be tested.

  1. Atoms are far too small to be seen directly, so scientists describe them using a scientific model built from experimental evidence.
  2. A good model explains all of the observations made so far and allows scientists to make predictions about new experiments.
  3. When an experiment produces a result that the current model cannot explain, the model has to be adapted or replaced by a better one.
  4. A new model is only accepted once other scientists have repeated the experiment, checked the results and agreed with the conclusions, a process called peer review.
  5. Each earlier model of the atom was a sensible explanation of the evidence available at the time, so it was replaced because of new evidence rather than because it was careless.
  6. The atomic model changed several times between the early 1800s and the 1930s, and each change was driven by a new discovery.

Dalton's solid sphere model

  1. In the early 1800s John Dalton described atoms as tiny solid spheres that could not be divided into anything smaller.
  2. In Dalton's model each element was made of its own type of atom, and atoms of different elements had different masses.
  3. This model explained how elements combine in fixed proportions, but it gave atoms no internal structure at all.

Thomson's plum pudding model

Definition

Electron

A tiny, negatively charged subatomic particle found outside the nucleus of an atom.

Definition

Plum pudding model

A model of the atom as a ball of positive charge with negatively charged electrons embedded throughout it.

  1. In 1897 J.J. Thomson discovered the electron, a particle with a negative charge and a mass far smaller than that of any atom.
  2. Because electrons could be removed from atoms, the atom could no longer be an indivisible solid sphere, so Dalton's model had to be replaced.
  3. Atoms are electrically neutral overall, so Thomson reasoned that there must also be positive charge in the atom to cancel the negative charge of the electrons.
  4. In his plum pudding model, the atom was a ball of evenly spread positive charge with negative electrons scattered through it, like dried fruit in a Christmas pudding.
  5. In this model the mass and the positive charge were spread evenly through the whole volume of the atom, with no dense centre.

The alpha particle scattering experiment

Definition

Alpha particle

A positively charged particle made of two protons and two neutrons, given out by some radioactive nuclei.

Definition

Nuclear model

A model of the atom as a tiny, positively charged nucleus holding almost all the mass, surrounded by electrons in mostly empty space.

  1. In 1909 Hans Geiger and Ernest Marsden, working under Ernest Rutherford, fired a narrow beam of alpha particles at a very thin sheet of gold foil inside a vacuum chamber.
  2. Gold was chosen because it can be hammered into a foil only a tiny fraction of a millimetre thick, so the alpha particles had very few atoms to pass through.
  3. The chamber had its air removed so that the alpha particles would not be stopped or scattered by air molecules before reaching the foil.
  4. A small zinc sulfide screen gave a tiny flash of light whenever an alpha particle struck it, and the screen was moved round the foil to count the flashes at each angle.
  5. If the plum pudding model were correct, the thinly spread positive charge would only nudge each fast alpha particle slightly, so every particle should have passed through with a very small deflection.
  6. Most alpha particles did pass straight through the foil undeflected, which showed that most of the atom is empty space.
  7. A small number were deflected through large angles, which showed that the positive charge is concentrated in a very small region that repels the positive alpha particles.
  8. A very few, roughly 1 in every 8000, bounced back towards the source, which showed that this small central region also contains most of the mass of the atom.
  9. In 1911 Rutherford explained these results with the nuclear model, in which a tiny, dense, positively charged nucleus sits at the centre with electrons moving around it.
  10. The plum pudding model could not explain the large deflections, so it was replaced by the nuclear model once other scientists had confirmed the results.
Example

Using scattering counts

  • In a repeat of the gold foil experiment, 400 000400\,000400000 alpha particles are fired at the foil.
  • About 1 alpha particle in every 800080008000 is scattered back through more than 90∘90^\circ90∘.
  • The number expected to bounce back is 400 0008000=50\dfrac{400\,000}{8000} = 508000400000​=50.
  • This leaves 399 950399\,950399950 alpha particles that pass through or are only deflected, which is more than 99.98%99.98\%99.98% of the beam.
  • The tiny fraction that bounces back is evidence that the nucleus occupies a very small part of the atom's volume.

Bohr's energy levels

Definition

Energy level

A fixed distance from the nucleus at which an electron can orbit with a particular amount of energy, also called a shell.

  1. Rutherford's nuclear model did not explain where the electrons are or why they stay in the atom.
  2. Heated gases give out light of only certain specific frequencies, and the nuclear model could not explain this pattern either.
  3. In 1913 Niels Bohr adapted the nuclear model by proposing that electrons orbit the nucleus at fixed distances, called energy levels or shells.
  4. An electron in a particular energy level has a fixed amount of energy, so it can only move to another level by absorbing or giving out an exact amount of energy.
  5. This explained the specific frequencies of light given out by each element, and Bohr's calculations agreed with the experimental measurements.
  6. Because the adapted model matched the evidence, the Bohr model was accepted and it is the picture of the atom still used at GCSE.

Protons and neutrons

Definition

Proton

A positively charged subatomic particle found in the nucleus of an atom.

Definition

Neutron

An uncharged subatomic particle found in the nucleus of an atom.

  1. Later experiments by Rutherford showed that the positive charge of a nucleus is carried by smaller particles, each with the same positive charge, which were named protons.
  2. The mass of most nuclei turned out to be greater than the mass of their protons alone, which suggested that the nucleus contained another particle.
  3. In 1932 James Chadwick provided experimental evidence for this particle, the neutron, which has no charge.
  4. Chadwick's discovery completed the model of a nucleus made of protons and neutrons, surrounded by electrons in energy levels.
Exam technique

Explaining a change in the model

  • Link every observation from the scattering experiment to its conclusion in the same sentence, using a word such as so or which shows that.
  • Match the three observations to the right conclusions: passing straight through means empty space, large deflections mean a concentrated positive charge, and bouncing back means most of the mass is in the nucleus.
  • When asked why the model changed, state that new evidence could not be explained by the old model, and that the new model explained it.
  • Keep the names in their correct roles: Geiger and Marsden carried out the experiment, while Rutherford interpreted the results.
  • For a sequence question, give the models in order with the discovery that caused each change: Dalton, then Thomson, then Rutherford, then Bohr, then Chadwick.
Common Mistake
  • Do not write that alpha particles hit the nucleus and bounced off it, because they are turned back by electrostatic repulsion between two positive charges.
  • Do not write that most alpha particles passed through the nucleus, because they passed through the empty space in the atom.
  • Do not describe the plum pudding model as having a nucleus, because the positive charge in that model is spread through the whole atom.
  • Do not call an alpha particle, a proton or an electron an atom, because each is a particle much smaller than an atom.
Self review
  • Describe the plum pudding model of the atom.
  • State why the discovery of the electron meant Dalton's model had to change.
  • Give the three observations of the alpha scattering experiment and what each one showed.
  • Explain why the plum pudding model predicted that alpha particles would pass through the foil with only very small deflections.
  • State what Bohr added to the nuclear model and the evidence it explained.

1.1.2 Structure of the atom

Parts of an atom

Definition

Atom

The smallest particle of an element, made of a positively charged nucleus surrounded by negatively charged electrons.

Definition

Nucleus

The tiny, positively charged centre of an atom that contains almost all of its mass.

Definition

Subatomic particle

A particle smaller than an atom, such as a proton, a neutron or an electron.

  1. Every atom has two regions: a central nucleus and the space around it in which the electrons move.
  2. The nucleus carries a positive charge and sits at the very centre of the atom.
  3. The nucleus is made of protons, which are positively charged, and neutrons, which have no charge.
  4. The electrons carry a negative charge and move around the nucleus in energy levels, also called shells.
  5. Protons, neutrons and electrons are all subatomic particles, because each is much smaller than the atom it belongs to.
  6. The positive nucleus and the negative electrons attract each other, and this electrostatic attraction holds the electrons in the atom.
  7. An atom has no overall charge, because the total negative charge of its electrons is equal in size to the total positive charge of its nucleus.

A diagram of an atom showing a central nucleus containing positively charged protons and neutral neutrons, with negatively charged electrons orbiting in shells.

Size of the nucleus

  1. The radius of the nucleus is much smaller than the radius of the whole atom.
  2. The radius of a nucleus is less than about one ten-thousandth of the radius of the atom it sits in.
  3. Almost all of the volume of an atom is therefore the region around the nucleus, where the electrons move through what is otherwise empty space.
  4. If an atom were scaled up to the size of a football stadium, the nucleus would be about the size of a pea on the centre spot.
  5. Diagrams of atoms, including the one above, are not drawn to scale, because a nucleus drawn at its true relative size would be too small to see.
Example

Scaling a model atom

  • A student makes a scale model of an atom using a bead of diameter 1 mm1\ \text{mm}1 mm as the nucleus.
  • The atom's radius is at least 10 00010\,00010000 times the nuclear radius, so the diameters are in the same ratio.
  • Diameter of the model atom =10 000×1 mm=10 000 mm= 10\,000 \times 1\ \text{mm} = 10\,000\ \text{mm}=10000×1 mm=10000 mm.
  • Converting to metres gives 10 000 mm÷1000=10 m10\,000\ \text{mm} \div 1000 = 10\ \text{m}10000 mm÷1000=10 m.
  • The model atom would need to be at least 10 m10\ \text{m}10 m across, larger than a classroom, to hold a nucleus the size of a bead.

Where the mass is

  1. Almost all of the mass of an atom is found in its nucleus.
  2. Protons and neutrons have very similar masses, and each is roughly 200020002000 times heavier than an electron.
  3. The electrons therefore add only a tiny amount to the mass of an atom, typically much less than 0.1%0.1\%0.1% of the total.
  4. This produces a striking contrast: the nucleus takes up almost none of the volume but holds almost all of the mass.
  5. The electron region is the opposite, taking up almost all of the volume but holding very little of the mass.
  6. Because so much mass is packed into such a small volume, the material of a nucleus is extremely dense.
Exam technique

Describing atomic structure

  • A full description of an atom needs three separate ideas: the charges and positions of the parts, the relative size of the nucleus and the location of the mass.
  • Write much smaller when comparing the nuclear radius with the atomic radius, because a bare smaller does not show the scale of the difference.
  • Write almost all of the mass is in the nucleus, because the electrons do have a small mass.
  • Name the charges with their signs, positive for the nucleus and negative for the electrons, rather than calling the parts simply charged.
Common Mistake
  • Do not write that the nucleus contains all of the mass of an atom, because the electrons contribute a very small amount.
  • Do not judge the size of a nucleus from a diagram, because diagrams exaggerate it so that it can be seen.
  • Do not describe the electrons as sitting inside the nucleus, because they move in energy levels well outside it.
  • Do not confuse the atom with its parts, because the nucleus and the electrons are pieces of one atom and are not atoms themselves.
Self review
  • State the charge of the nucleus and the charge of an electron.
  • Name the two types of particle found in the nucleus.
  • Explain why an atom has no overall charge.
  • Compare the radius of the nucleus with the radius of the atom.
  • State where almost all of the mass of an atom is found and explain why the electrons add so little.

1.1.3 The size of atoms and small molecules

Typical size of atoms

Definition

Molecule

A particle made of two or more atoms chemically bonded together.

  1. Atoms and small molecules are extremely small, with a typical diameter of about 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m.
  2. Written out in full, 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m is 0.0000000001 m0.0000000001\ \text{m}0.0000000001 m, which is one ten-billionth of a metre.
  3. This value can also be written as 0.1 nm0.1\ \text{nm}0.1 nm, because one nanometre is 1×10−9 m1 \times 10^{-9}\ \text{m}1×10−9 m.
  4. Different atoms do have slightly different sizes, but almost all of them have diameters between about 0.5×10−10 m0.5 \times 10^{-10}\ \text{m}0.5×10−10 m and 5×10−10 m5 \times 10^{-10}\ \text{m}5×10−10 m, so they share the same order of magnitude.
  5. A small molecule, such as a water molecule made of three atoms, is only a few atoms across, so it has a size on the same scale of about 10−10 m10^{-10}\ \text{m}10−10 m.
  6. Large molecules, such as proteins or plastics, contain thousands of atoms and are much bigger, so the value 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m only applies to atoms and small molecules.
  7. Atoms are far smaller than the wavelength of visible light, so they cannot be seen with an ordinary light microscope.

Orders of magnitude

Definition

Order of magnitude

The power of ten closest to the size of a quantity.

Definition

Standard form

A way of writing a number as a value from 1 up to, but not including, 10 multiplied by a power of ten.

  1. Very large and very small quantities are compared using their order of magnitude, which is the power of ten closest to the quantity.
  2. The order of magnitude of an atom is 10−10 m10^{-10}\ \text{m}10−10 m.
  3. Numbers of this size are written in standard form, with a number from 111 up to, but not including, 101010 multiplied by a power of ten.
  4. A negative power of ten shows a number smaller than 111, and the more negative the power, the smaller the number.
  5. Two quantities differ by one order of magnitude when one is about 101010 times the other, and by two orders of magnitude when one is about 100100100 times the other.
  6. To find how many orders of magnitude separate two quantities, subtract the power of ten of the smaller one from the power of ten of the larger one.
Example

Converting a molecule size

  • A small molecule has a measured width of 0.28 nm0.28\ \text{nm}0.28 nm.
  • Using 1 nm=1×10−9 m1\ \text{nm} = 1 \times 10^{-9}\ \text{m}1 nm=1×10−9 m, the width is 0.28×10−9 m0.28 \times 10^{-9}\ \text{m}0.28×10−9 m.
  • In standard form this becomes 2.8×10−10 m2.8 \times 10^{-10}\ \text{m}2.8×10−10 m.
  • The nearest power of ten is 10−10 m10^{-10}\ \text{m}10−10 m, so the molecule has the typical order of magnitude of a small molecule.

Comparing sizes

  1. A human hair has a width of about 1×10−4 m1 \times 10^{-4}\ \text{m}1×10−4 m, which is six orders of magnitude larger than an atom.
  2. This means roughly one million atoms would fit side by side across the width of a single hair.
  3. A grain of fine sand is about 1×10−4 m1 \times 10^{-4}\ \text{m}1×10−4 m to 1×10−3 m1 \times 10^{-3}\ \text{m}1×10−3 m across, so even the smallest speck visible to the eye contains an enormous number of atoms.
  4. A nucleus, with a radius of around 10−14 m10^{-14}\ \text{m}10−14 m to 10−15 m10^{-15}\ \text{m}10−15 m, is four to five orders of magnitude smaller than the atom it sits in.
Example

Atoms across a millimetre

  • A line 1 mm1\ \text{mm}1 mm long is drawn in pencil, which is 1×10−3 m1 \times 10^{-3}\ \text{m}1×10−3 m.
  • Each atom has a typical diameter of 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m.
  • Number of atoms along the line =1×10−31×10−10= \dfrac{1 \times 10^{-3}}{1 \times 10^{-10}}=1×10−101×10−3​.
  • Dividing powers of ten means subtracting the indices, so 10−3−(−10)=10710^{-3-(-10)} = 10^{7}10−3−(−10)=107.
  • About 1×1071 \times 10^{7}1×107, or ten million, atoms would fit side by side along the line.
Exam technique

Recalling the size of an atom

  • When asked for the typical size of an atom or small molecule, give 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m and always include the unit.
  • In a multiple choice question, check the sign of the power, because 1×1010 m1 \times 10^{10}\ \text{m}1×1010 m is a huge distance, not a tiny one.
  • When comparing sizes, divide the larger value by the smaller one and state the answer as a number of times or as a number of orders of magnitude.
  • Show the division of powers of ten on the page, because the working can earn credit even if the final value is wrong.
Common Mistake
  • Do not confuse the size of an atom, about 10−10 m10^{-10}\ \text{m}10−10 m, with the much smaller size of its nucleus.
  • Do not write the power of ten as positive, because 101010^{10}1010 is ten billion, not one ten-billionth.
  • Do not describe atoms as the size of dust or specks, because even the smallest visible particle contains billions of atoms.
Self review
  • State the typical size of an atom in metres.
  • Write 1×10−10 m1 \times 10^{-10}\ \text{m}1×10−10 m in nanometres.
  • Explain what is meant by the order of magnitude of a length.
  • Calculate how many orders of magnitude separate a hair of width 10−4 m10^{-4}\ \text{m}10−4 m from an atom.
  • Explain why the value 10−10 m10^{-10}\ \text{m}10−10 m does not apply to large molecules such as proteins.

1.1.4 Density

What density means

Definition

Density

The mass per unit volume of a material.

Definition

Mass

The amount of matter in an object, measured in kilograms.

Definition

Volume

The amount of space that an object or substance takes up, measured in cubic metres.

  1. Density measures how much mass is packed into each unit of volume of a material.
  2. A material with a high density has a large mass in a small volume, while a material with a low density has a small mass spread through a large volume.
  3. A 1 kg1\ \text{kg}1 kg bag of sugar and a 1 kg1\ \text{kg}1 kg bag of crisps have the same mass, but the crisps fill a much larger volume, so they have a much lower density.
  4. Density is a property of the material, not of the object, so a steel paper clip and a steel girder have the same density even though their masses are very different.
  5. Density is found using the equation ρ=mV\rho = \dfrac{m}{V}ρ=Vm​, where ρ\rhoρ is density, mmm is mass and VVV is volume.
  6. In words, the equation is density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}density=volumemass​, and it must be recalled rather than looked up.
  7. The equation can be rearranged to m=ρVm = \rho Vm=ρV to find a mass, or to V=mρV = \dfrac{m}{\rho}V=ρm​ to find a volume.

Units of density

  1. The SI unit of density is the kilogram per cubic metre, written kg/m3\text{kg/m}^3kg/m3, which comes from mass in kg\text{kg}kg divided by volume in m3\text{m}^3m3.
  2. In the laboratory, density is often given in grams per cubic centimetre, written g/cm3\text{g/cm}^3g/cm3, which comes from mass in g\text{g}g divided by volume in cm3\text{cm}^3cm3.
  3. A cube of side 1 m1\ \text{m}1 m contains 100×100×100=1 000 000100 \times 100 \times 100 = 1\,000\,000100×100×100=1000000 cubes of side 1 cm1\ \text{cm}1 cm, so 1 m3=1×106 cm31\ \text{m}^3 = 1 \times 10^{6}\ \text{cm}^31 m3=1×106 cm3.
  4. A density of 1 g/cm31\ \text{g/cm}^31 g/cm3 is equal to 1000 kg/m31000\ \text{kg/m}^31000 kg/m3, so a value in g/cm3\text{g/cm}^3g/cm3 is multiplied by 100010001000 to give it in kg/m3\text{kg/m}^3kg/m3.
  5. Pure water has a density of about 1000 kg/m31000\ \text{kg/m}^31000 kg/m3, aluminium about 2700 kg/m32700\ \text{kg/m}^32700 kg/m3, steel about 7900 kg/m37900\ \text{kg/m}^37900 kg/m3 and air about 1.2 kg/m31.2\ \text{kg/m}^31.2 kg/m3.
  6. The mass and the volume must be in matching units before dividing, so a mass in grams is never divided by a volume in cubic metres.
Example

Density of a stone

  • A stone has a mass of 0.60 kg0.60\ \text{kg}0.60 kg and a volume of 2.4×10−4 m32.4 \times 10^{-4}\ \text{m}^32.4×10−4 m3.
  • Write the equation: ρ=mV\rho = \dfrac{m}{V}ρ=Vm​.
  • Substitute the values: ρ=0.602.4×10−4\rho = \dfrac{0.60}{2.4 \times 10^{-4}}ρ=2.4×10−40.60​.
  • Calculate the result: ρ=2500 kg/m3\rho = 2500\ \text{kg/m}^3ρ=2500 kg/m3.
Example

Mass of air in a classroom

  • A classroom measures 8.0 m8.0\ \text{m}8.0 m by 6.0 m6.0\ \text{m}6.0 m by 3.0 m3.0\ \text{m}3.0 m, and air has a density of 1.2 kg/m31.2\ \text{kg/m}^31.2 kg/m3.
  • Find the volume: V=8.0×6.0×3.0=144 m3V = 8.0 \times 6.0 \times 3.0 = 144\ \text{m}^3V=8.0×6.0×3.0=144 m3.
  • Rearrange the density equation: m=ρVm = \rho Vm=ρV.
  • Substitute the values: m=1.2×144=172.8 kgm = 1.2 \times 144 = 172.8\ \text{kg}m=1.2×144=172.8 kg.
  • To two significant figures the air in the room has a mass of 170 kg170\ \text{kg}170 kg, which is more than the mass of two adults.

Measuring mass and volume

Definition

Water displacement

A method of finding the volume of an object from the volume of water it pushes aside when fully submerged.

Definition

Meniscus

The curved surface of a liquid in a narrow container such as a measuring cylinder.

Definition

Upthrust

The upward force that a fluid exerts on an object that is partly or fully submerged in it.

  1. Mass is measured with a top-pan balance, which should be set to zero before the object is placed on it.
  2. The volume of a regular solid, such as a cube, cuboid or cylinder, is calculated from its measured dimensions.
  3. The volume of an irregular solid, such as a stone or a key, is found by water displacement, because a fully submerged object pushes aside a volume of water equal to its own volume.
  4. The volume of a liquid is read directly from a measuring cylinder, looking at the bottom of the meniscus with the eye level with the liquid surface.
  5. Reading the scale from above or below eye level causes a parallax error, which makes every reading too high or too low.
  6. When an object is lowered into water, the water pushes up on it with a force called upthrust, which is why objects feel lighter when submerged.
Practical

Determining the density of solids and liquids

  • Aim: to determine the densities of a regular solid, an irregular solid and a liquid by measuring their mass and volume.
  • Apparatus: top-pan balance reading to 0.01 g0.01\ \text{g}0.01 g, ruler with a millimetre scale, vernier callipers, a metal cuboid, a small irregular stone, a eureka can, a 100 cm3100\ \text{cm}^3100 cm3 measuring cylinder, a 250 cm3250\ \text{cm}^3250 cm3 beaker, thread, a supply of water, the liquid to be tested and paper towels.
  • Method, regular solid:
    • Zero the balance, place the metal cuboid in the centre of the pan and record its mass in grams.
    • Measure the length, width and height of the cuboid with vernier callipers, closing the jaws gently so that they touch the metal without squeezing it.
    • Measure each dimension in three different places and calculate a mean, because the block may not be perfectly even.
    • Calculate the volume in cm3\text{cm}^3cm3 using V=length×width×heightV = \text{length} \times \text{width} \times \text{height}V=length×width×height, then calculate the density using ρ=mV\rho = \dfrac{m}{V}ρ=Vm​.
  • Method, irregular solid:
    • Zero the balance, dry the stone with a paper towel and record its mass.
    • Stand the eureka can on a level bench and fill it with water until water starts to run out of the spout.
    • Wait until the dripping has completely stopped, so that the water surface sits exactly level with the bottom of the spout.
    • Place the empty measuring cylinder under the spout.
    • Tie the thread around the stone and lower it slowly into the eureka can until it is fully submerged, without splashing and without letting it touch the sides.
    • Wait until water has stopped dripping from the spout, then read the volume of water in the measuring cylinder at eye level from the bottom of the meniscus.
    • Record this volume as the volume of the stone, then calculate its density using ρ=mV\rho = \dfrac{m}{V}ρ=Vm​.
  • Method, liquid:
    • Place the empty, dry measuring cylinder on the balance and record its mass.
    • Pour about 50 cm350\ \text{cm}^350 cm3 of the liquid into the cylinder and read its exact volume at eye level from the bottom of the meniscus.
    • Put the cylinder back on the balance and record the combined mass of the cylinder and the liquid.
    • Subtract the mass of the empty cylinder from the combined mass to find the mass of the liquid.
    • Add further 10 cm310\ \text{cm}^310 cm3 portions of liquid, recording the total volume and combined mass each time, and calculate the density for every reading.
  • Results: record every measurement in a table with the quantity and its unit in each column heading, and give each density to a consistent number of significant figures.
  • Maths: for the liquid, plot mass on the yyy-axis against volume on the xxx-axis, and the gradient of the straight line through the origin gives the density of the liquid.
  • Watch out: air bubbles clinging to the stone make the displaced volume too large, water left in the spout from filling makes it too small, and a wet stone gives a mass that is too large.
  • Safety: mop up spilled water straight away so no one slips, keep the balance away from the water, and wear eye protection if the test liquid is anything other than water.
Practical

Investigating Archimedes' principle

  • Aim: to compare the upthrust on a submerged object with the weight of the water it displaces.
  • Apparatus: a 000 to 10 N10\ \text{N}10 N newton meter, a metal mass of about 500 g500\ \text{g}500 g with a hook, a eureka can, a small beaker, a top-pan balance, a clamp stand and a supply of water.
  • Method:
    • Zero the newton meter, hang the metal mass from it and record the weight of the mass in air.
    • Find the mass of the empty, dry beaker on the balance and record it.
    • Fill the eureka can until water runs from the spout, wait for the dripping to stop, then place the beaker under the spout.
    • Lower the mass on the newton meter slowly into the eureka can until it is completely under water but not touching the bottom or sides.
    • Record the new reading on the newton meter while the mass is submerged and still.
    • When the dripping stops, find the mass of the beaker and the displaced water, then subtract the mass of the empty beaker.
    • Convert the mass of displaced water into kilograms and multiply by 10 N/kg10\ \text{N/kg}10 N/kg to find its weight.
  • Results: the upthrust is the weight in air minus the reading when submerged, and this value should be very close to the weight of the displaced water.
  • Maths: if the reading falls from 5.0 N5.0\ \text{N}5.0 N to 4.4 N4.4\ \text{N}4.4 N, the upthrust is 0.6 N0.6\ \text{N}0.6 N, and the displaced water should have a mass of about 60 g60\ \text{g}60 g.
  • Watch out: the newton meter must be read at eye level while the mass is still, and any water lost by splashing makes the displaced weight too small.
  • Safety: clamp the stand firmly to the bench so that the heavy mass cannot fall on your feet, and keep water away from any electrical sockets.
Exam technique

Describing a density method

  • Name the measuring instrument for each quantity, such as a balance for mass and a measuring cylinder or eureka can for volume.
  • State clearly that the volume of water displaced is equal to the volume of the object.
  • Finish every method with the calculation step, writing out ρ=mV\rho = \dfrac{m}{V}ρ=Vm​.
  • Give an improvement with its reason, for example repeating each reading and calculating a mean to reduce the effect of random errors.
  • In a calculation, show the equation, the substituted numbers and the answer with its unit, because each stage can earn credit.
Common Mistake
  • Do not confuse mass with density, because a large wooden log can have a greater mass than a steel bolt while having a much lower density.
  • Do not divide a mass in grams by a volume in cubic metres, because the units must match before the calculation.
  • Do not start collecting water from a eureka can until it has stopped dripping after filling, or the measured volume will be too large.
  • Do not forget that 1 m31\ \text{m}^31 m3 is one million cubic centimetres, not one hundred.
Self review
  • Define density.
  • Write the equation linking density, mass and volume, and rearrange it to make volume the subject.
  • Convert a density of 2.7 g/cm32.7\ \text{g/cm}^32.7 g/cm3 into kg/m3\text{kg/m}^3kg/m3.
  • Describe how the volume of an irregular solid is measured using a eureka can.
  • Explain why the bottom of the meniscus should be read at eye level.

1.1.5 Density and the states of matter

Particles and density

Definition

Particle model

A model in which all matter is made of tiny particles whose arrangement and movement explain the properties of solids, liquids and gases.

  1. The particle model describes every substance as a huge number of tiny particles, which are atoms in some substances and molecules in others.
  2. When a substance changes from one state to another, its particles stay the same particles with the same mass, and only their arrangement and spacing change.
  3. The density of a state therefore depends on how closely the particles are packed.
  4. The fairest way to compare states is to imagine the same volume of each, such as a 1 cm31\ \text{cm}^31 cm3 box filled with the solid, the liquid or the gas.
  5. If the particles are packed more closely, more particles fit inside the box, so the box contains more mass and the state has a higher density.
  6. If the particles are spread further apart, fewer particles fit inside the box, so the box contains less mass and the state has a lower density.
  7. The gaps between particles contain nothing at all, so they add volume without adding any mass.

Solids, liquids and gases

Definition

Solid

A state of matter in which the particles are packed closely in a regular arrangement and vibrate about fixed positions.

Definition

Liquid

A state of matter in which the particles are close together in an irregular arrangement and can move past one another.

Definition

Gas

A state of matter in which the particles are far apart in a random arrangement and move quickly in all directions.

Particle arrangement in solids, liquids, and gases. Solids are regular and closely packed; liquids are irregular and close; gases are random and far apart. Arrows show that temperature and molecular motion increase from solid to gas, while molecular interactions increase from gas to solid.

  1. In a solid, the particles are packed very closely in a regular arrangement and vibrate about fixed positions.
  2. So many particles fit into each unit of volume that solids usually have the highest density of the three states.
  3. In a liquid, the particles are still close together and touching, but they are arranged irregularly and can move past one another.
  4. The irregular arrangement leaves slightly more space than the ordered packing of a solid, so a liquid is usually slightly less dense than the solid of the same substance.
  5. For many metals the liquid is only a few per cent less dense than the solid, because the particle spacing hardly changes on melting.
  6. In a gas, the particles are far apart in a random arrangement, with distances between them many times larger than the particles themselves.
  7. A given volume of gas contains very few particles, so a gas has a very low density, typically around a thousand times lower than the liquid.
  8. Liquid water has a density of about 1000 kg/m31000\ \text{kg/m}^31000 kg/m3, while steam at 100 ∘C100\ ^\circ\text{C}100 ∘C has a density of only about 0.6 kg/m30.6\ \text{kg/m}^30.6 kg/m3.
  9. For most substances the order from highest to lowest density is therefore solid, then liquid, then gas.
Example

Same volume, different states

  • A 2.0 m32.0\ \text{m}^32.0 m3 tank is filled first with liquid water and then with steam.
  • Liquid water has a density of 1000 kg/m31000\ \text{kg/m}^31000 kg/m3, so its mass is m=ρV=1000×2.0=2000 kgm = \rho V = 1000 \times 2.0 = 2000\ \text{kg}m=ρV=1000×2.0=2000 kg.
  • Steam has a density of 0.6 kg/m30.6\ \text{kg/m}^30.6 kg/m3, so its mass is m=0.6×2.0=1.2 kgm = 0.6 \times 2.0 = 1.2\ \text{kg}m=0.6×2.0=1.2 kg.
  • The liquid has about 170017001700 times more mass in the same volume, because its molecules are packed so much more closely.

Water and ice

  1. Water is an important exception to the usual pattern, because solid ice is less dense than liquid water.
  2. When water freezes, its molecules lock into an open, regular structure that holds them slightly further apart than in the liquid.
  3. Ice has a density of about 920 kg/m3920\ \text{kg/m}^3920 kg/m3, which is lower than the 1000 kg/m31000\ \text{kg/m}^31000 kg/m3 of liquid water.
  4. This is why ice cubes float in a drink and why ponds freeze from the top downwards, leaving liquid water underneath.
  5. The explanation still uses the same idea as every other substance: the molecules in ice are spaced further apart, so there is less mass in each unit of volume.
Exam technique

Explaining density differences

  • Build the answer as a chain: the spacing of the particles, then the number of particles in the same volume, then the mass in that volume, then the density.
  • Always compare the same volume of each state, because density is about mass in a given volume, not about the size of the sample.
  • Use the words atoms or molecules where the question names the substance, and particles when it does not.
  • Describe both the arrangement and the spacing, for example regular and close together for a solid.
Common Mistake
  • Do not write that the particles in a gas are lighter, smaller or less dense than in a liquid, because the particles themselves do not change.
  • Do not say that the spaces between gas particles are filled with air, because the spaces are empty.
  • Do not state that a solid is always denser than its liquid, because ice is less dense than water.
  • Do not describe liquid particles as far apart, because they are almost as close together as in a solid.
Self review
  • Describe the arrangement of particles in a solid, a liquid and a gas.
  • Explain, in terms of particles, why a gas is much less dense than a liquid.
  • State why a liquid is usually slightly less dense than the solid of the same substance.
  • Explain why ice floats on liquid water.
  • State what is found in the spaces between the particles of a gas.

1.1.6 Density, mass and volume

Conservation of mass

Definition

Conservation of mass

The principle that the total mass of a closed system stays the same when its material changes shape, state or volume.

Definition

Closed system

A system that no matter can enter or leave.

  1. Particles cannot be created or destroyed when a material is squashed, stretched, heated, cooled, melted or frozen.
  2. If no material enters or leaves, the number of particles stays the same, so the mass stays the same.
  3. This idea is called conservation of mass, and it applies to any closed system.
  4. A sealed syringe of air, a block of ice melting in a sealed bag and a lump of clay being reshaped are all examples of closed systems.
  5. Many changes still alter the volume of a material, because the particles move closer together or further apart.
  6. A change in volume with no change in mass must therefore produce a change in density.

How volume affects density

Definition

Inverse proportion

A relationship between two quantities in which one halves when the other doubles, because their product stays constant.

  1. For a fixed mass, the density equation ρ=mV\rho = \dfrac{m}{V}ρ=Vm​ shows that density and volume are inversely proportional.
  2. If the same mass takes up a larger volume, the density decreases, because the mass is divided by a bigger number.
  3. If the same mass takes up a smaller volume, the density increases, because the mass is divided by a smaller number.
  4. Doubling the volume of a fixed mass halves its density, and halving the volume doubles its density.
  5. Since the mass is the same before and after the change, ρ1V1=ρ2V2\rho_1 V_1 = \rho_2 V_2ρ1​V1​=ρ2​V2​, where the subscripts 111 and 222 label the values before and after.
  6. Changing only the shape of a solid, such as rolling clay into a snake, keeps both its mass and its volume the same, so its density does not change.
  7. Cutting a block in half halves both its mass and its volume, so each piece still has the same density as the whole block.

Examples of conserved mass

  1. When a gas is compressed in a sealed syringe, its particles are pushed closer together, so its volume falls and its density rises.
  2. When air in a hot air balloon is heated, it expands, so the same mass fills a larger volume and its density falls.
  3. When water freezes, its volume increases by about 9%9\%9%, so the ice formed is less dense than the water it came from.
  4. When most other liquids freeze, their volume decreases slightly, so the solid formed is slightly denser than the liquid.
  5. When water boils, the same mass of water becomes steam with a volume about 170017001700 times larger, so its density falls by the same factor.
  6. In every case, the mass of the material before the change is used as the mass after the change.
Example

Water freezing in a bottle

  • A bottle holds 900 cm3900\ \text{cm}^3900 cm3 of water of density 1.00 g/cm31.00\ \text{g/cm}^31.00 g/cm3, and the water freezes into ice of density 0.92 g/cm30.92\ \text{g/cm}^30.92 g/cm3.
  • Find the mass of the water: m=ρV=1.00×900=900 gm = \rho V = 1.00 \times 900 = 900\ \text{g}m=ρV=1.00×900=900 g.
  • The bottle is sealed, so the mass of the ice is also 900 g900\ \text{g}900 g.
  • Find the volume of the ice: V=mρ=9000.92=978 cm3V = \dfrac{m}{\rho} = \dfrac{900}{0.92} = 978\ \text{cm}^3V=ρm​=0.92900​=978 cm3.
  • The volume increases by about 80 cm380\ \text{cm}^380 cm3, which is why a full glass bottle of water can crack in a freezer.
Example

Compressing air in a syringe

  • A sealed syringe contains 0.060 g0.060\ \text{g}0.060 g of air in a volume of 50 cm350\ \text{cm}^350 cm3.
  • The density before compression is ρ=0.06050=0.0012 g/cm3\rho = \dfrac{0.060}{50} = 0.0012\ \text{g/cm}^3ρ=500.060​=0.0012 g/cm3.
  • The plunger is pushed in until the volume is 20 cm320\ \text{cm}^320 cm3, and no air escapes, so the mass is still 0.060 g0.060\ \text{g}0.060 g.
  • The density after compression is ρ=0.06020=0.0030 g/cm3\rho = \dfrac{0.060}{20} = 0.0030\ \text{g/cm}^3ρ=200.060​=0.0030 g/cm3.
  • The volume has been divided by 2.52.52.5, so the density has been multiplied by 2.52.52.5.
Example

Heating air in a balloon

  • Air in a balloon has a density of 1.20 kg/m31.20\ \text{kg/m}^31.20 kg/m3, and heating it increases its volume by 25%25\%25% with no air escaping.
  • The new volume is 1.251.251.25 times the original volume, so ρ2=ρ1V1V2=1.201.25\rho_2 = \dfrac{\rho_1 V_1}{V_2} = \dfrac{1.20}{1.25}ρ2​=V2​ρ1​V1​​=1.251.20​.
  • The new density is ρ2=0.96 kg/m3\rho_2 = 0.96\ \text{kg/m}^3ρ2​=0.96 kg/m3.
  • The heated air is less dense than the cooler air outside, which is what allows a hot air balloon to rise.
Exam technique

Changes where mass is conserved

  • Look for words such as sealed, no material is lost or the same object, which tell you to use the same mass before and after the change.
  • Work out the mass first from the starting density and volume, then use it with the new volume or new density.
  • State the direction of the change in words as well as numbers, for example the volume increases so the density decreases.
  • Keep the units consistent throughout, using either g\text{g}g with cm3\text{cm}^3cm3 or kg\text{kg}kg with m3\text{m}^3m3.
Common Mistake
  • Do not assume that a change in volume means a change in mass, because the number of particles stays the same in a closed system.
  • Do not say that the density of a piece changes when a block is cut, because the mass and volume fall by the same factor.
  • Do not say that particles expand when a material is heated, because it is the spaces between the particles that increase.
  • Do not use a new mass after a change of state unless the question says that material has been added or lost.
Self review
  • State what is meant by conservation of mass.
  • Describe what happens to the density of a fixed mass of gas when its volume is halved.
  • Explain why cutting a metal block in half does not change its density.
  • Explain why a sealed bottle full of water can crack when the water freezes.
  • Calculate the new density of 0.080 g0.080\ \text{g}0.080 g of air compressed from 40 cm340\ \text{cm}^340 cm3 to 10 cm310\ \text{cm}^310 cm3.

How was this guide?

Teach Genie

Review 1.1 The particle model by teaching Genie

Teach it back in your own words, spot gaps, and remember it better.

Start teaching
Genie and Baby Genie

Lesson

Recap your knowledge with an interactive lesson

8 minute activity

Start lesson

Particle model comparison of solid, liquid, and gas showing spacing, arrangement, motion, and relative density

Matter is anything that has mass and takes up space. A particle is a tiny piece of matter, and in the particle model the arrangement and motion of particles explain the properties of solids, liquids, and gases.

In solids, particles are close together in a regular arrangement and only vibrate about fixed positions. In liquids, particles are still close together but can move past each other, while in gases they are far apart and move rapidly in random directions.

Because gas particles are much more spread out, gases usually have much lower density than liquids and solids. The particle model is a scientific model, so it is a simplified picture used to explain evidence.

Questions

Put it into practice with exam-style questions

44 exam-style questions

Practice questions

Question 1

5 marks

The Figure shows the nuclear model of an atom.

Figure

Flashcards

Remember key concepts with flashcards

29 flashcards

Practice flashcards

What is matter in physics?

1.1 The particle model Revision Guide

  1. GCSE
  2. /Physics
  3. /1.1 The particle model

Revision notes for OCR GCSE Physics 1.1 The particle model: explanations and worked examples on 1.1.1 Development of the atomic model, 1.1.2 Structure of the atom, 1.1.3 The size of atoms and small molecules, 1.1.4 Density, 1.1.5 Density and the states of matter, and 1.1.6 Density, mass and volume.

Revision guides