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Physics · 5 Nuclear physics

5.1.2 The nucleus

Before you start

  • The nuclear model of the atom: a very small, positively charged nucleus with negatively charged electrons in orbit around it (5.1.1).
  • That a neutral atom has no overall charge, and that an ion forms when an atom loses or gains electrons (5.1.1).
  • That like charges repel and unlike charges attract.
  • That energy is never created or destroyed, only transferred from one store to another.
Syllabus objectives covered (8)
  • Describe the composition of the nucleus in terms of protons and neutrons
  • State the relative charges of protons, neutrons and electrons as +1, 0 and –1 respectively
  • Define the terms proton number (atomic number) Z and nucleon number (mass number) A and be able to calculate the number of neutrons in a nucleus
  • Use the nuclide notation A ZX
  • Explain what is meant by an isotope and state that an element may have more than one isotope
  • Describe the processes of nuclear fission and nuclear fusion as the splitting or joining of nuclei, to include the nuclide equation and qualitative description of mass and energy changes without values
  • Know the relationship between the proton number and the relative charge on a nucleus
  • Know the relationship between the nucleon number and the relative mass of a nucleus

Part 1 of 8

Inside the nucleus: protons and neutrons

  1. In 5.1.1 you met the nucleus as the tiny, positively charged centre of the atom, with electrons in orbit around it. This subtopic opens the nucleus up and asks what it is made of.
  2. A nucleus is made of two kinds of particle: protons and neutrons. Together they are called nucleons. A nucleon is simply any particle that is found in the nucleus.
  3. Electrons are not in the nucleus. They orbit outside it. Hold on to this, because every count you make in this subtopic is a count of what is inside the nucleus, and electrons never appear in it.
    apparatus diagram — not drawn yet

    A lithium-7 atom: a central nucleus drawn as a tight cluster of 3 protons marked + and 4 neutrons left unmarked, with 3 electrons marked − on orbits around it; the nucleus is labelled and drawn much larger than to scale, and beside the atom is the nuclide symbol Li with 7 at the top left and 3 at the bottom left.

    Count the cluster: 3 protons gives the bottom number 3; 3 protons + 4 neutrons = 7 nucleons gives the top number 7. The electrons are outside and are in neither count.
  4. There is one nucleus with no neutrons: hydrogen-1, the ordinary form of hydrogen. Its nucleus is a single proton. Every other nucleus contains both protons and neutrons.
  5. Each particle has a relative charge: its charge compared with the size of the charge on a proton. The three values you must state are: proton +1, neutron 0, electron −1.
  6. The proton and the electron have charges that are equal in size and opposite in sign. That is why a neutral atom, which has equal numbers of protons and electrons, has no overall charge.
  7. The neutron has no charge at all. The name is the reminder: a neutron is neutral. So the whole positive charge of a nucleus comes from its protons.

Part 2 of 8

Proton number, nucleon number and counting neutrons

  1. Two numbers describe any nucleus. Learn the definition of each word for word, because Define means give the precise meaning, and a definition that leaves out a part is not precise.
  2. The proton number (atomic number), Z, is the number of protons in the nucleus.
  3. The nucleon number (mass number), A, is the total number of protons and neutrons in the nucleus. In other words, it is the number of nucleons.
  4. Notice that both definitions end with 'in the nucleus'. Electrons are not part of either number.
  5. The proton number decides which element the atom is. Every carbon nucleus has 6 protons, and any nucleus with 6 protons is carbon. Change the number of protons and you have a different element.
  6. In a neutral atom the number of electrons is equal to the number of protons, so a neutral atom also has Z electrons. In an ion this is no longer true, because electrons have been lost or gained.
  7. The number of neutrons is not written anywhere, so you calculate it. A counts the protons plus the neutrons, so take the protons away and the neutrons are what is left. Here N is the number of neutrons:
    N=A−Z
  8. The trap here is to read A as the number of neutrons. A nucleus with A=23 and Z=11 has 23−11=12 neutrons, not 23.
  9. A quick sense check on any answer: A can never be smaller than Z, because A counts the protons and then adds the neutrons on top.

Part 3 of 8

Nuclide notation

  1. Nuclide notation puts both numbers on one symbol. The nucleon number A goes at the top left, the proton number Z at the bottom left, and the chemical symbol of the element, written here as X, goes on the right:
    ZAX
  2. Read 614C like this: the element is carbon; there are 6 protons; there are 14 nucleons; so there are 14−6=8 neutrons.
  3. Going the other way, a nucleus of nitrogen (symbol N) with 7 protons and 8 neutrons has A=7+8=15, so you write it as 715N. Add the protons and neutrons for the top number; the protons alone give the bottom number.
  4. For a nucleus, the top number is never smaller than the bottom number; they are equal only for 11H. If you have written the smaller number on top, you have swapped them.
  5. Nuclides are also named in words: the element, then the nucleon number. Carbon-14 is 614C and uranium-235 is 92235U. The word form tells you A only, so to count neutrons you also need Z.
  6. Single particles get the same style of symbol. A neutron is 01n: one nucleon, no charge. A proton is 11p: one nucleon, charge +1. You will need the neutron symbol for the fission and fusion equations later in this lesson.
  7. An electron is written −10e. It is not a nucleon, so its top number is 0, and its bottom number is its relative charge, −1.
  8. That last symbol shows something useful. In this notation the bottom number is always the relative charge. For a nucleus that is the same as the proton number, because the protons are the only charged particles in it.

Part 4 of 8

Isotopes

  1. The proton number fixes the element, so two nuclei of the same element must have the same number of protons. Nothing says they must have the same number of neutrons.
  2. Isotopes are atoms of the same element that have different numbers of neutrons. They have the same proton number and different nucleon numbers.
  3. An element may have more than one isotope. Carbon, for example, has the isotopes carbon-12, carbon-13 and carbon-14. All three have 6 protons; they have 6, 7 and 8 neutrons.
    612C613C614C
  4. Hydrogen has isotopes too: 11H with no neutrons, 12H with one neutron and 13H with two neutrons. Hydrogen-2 and hydrogen-3 appear again in the fusion equations below.
  5. To test whether two nuclides are isotopes, compare the bottom numbers first. If they differ, the nuclides are different elements and cannot be isotopes, whatever their top numbers. If the bottom numbers match and the top numbers differ, they are isotopes.
  6. The trap here is a matching top number. 1840Ar and 2040Ca both have 40 nucleons, but they have 18 and 20 protons, so they are two different elements and not isotopes.
  7. Isotopes are not ions either. Isotopes of an element differ in the number of neutrons, which are inside the nucleus. Ions of an element differ in the number of electrons, which are outside it.
  8. When you explain what an isotope is, give both halves: the same number of protons and a different number of neutrons. 'Different number of neutrons' alone does not say that the atoms are the same element, and 'same number of protons' alone describes every atom of that element.

Part 5 of 8

What the two numbers tell you about charge and mass

  1. The charge on a nucleus comes only from its protons, because neutrons are uncharged. Each proton gives +1, so the relative charge on a nucleus is equal to its proton number.
  2. Written as a relationship:
    relative charge on a nucleus=+Z
  3. So a 92238U nucleus has a relative charge of +92, and a 614C nucleus has a relative charge of +6.
  4. Now the mass. Protons and neutrons have almost exactly the same mass, so each nucleon is given a relative mass of 1. A nucleus with A nucleons therefore has a relative mass approximately equal to A.
  5. Written as a relationship:
    relative mass of a nucleus≈A
  6. Electrons are left out of this because they are not in the nucleus. They hardly change the mass of the whole atom either: an electron's mass is only about 11840 of a proton's mass.
  7. So nuclide notation is also a label for charge and mass. The bottom number is the relative charge on the nucleus, and the top number is approximately its relative mass. 92238U: relative charge +92, relative mass about 238.
  8. Apply this to isotopes. Isotopes of an element have the same charge on the nucleus but different masses. 1735Cl and 1737Cl both carry +17, and the second is heavier, with a relative mass of about 37 against about 35.
  9. Keep the word approximately. The relative mass of a nucleus is close to A, but not exactly A. That small gap is what allows the mass to change in fission and fusion while the nucleon numbers still balance, as you will see below.

Part 6 of 8

Nuclear fission: splitting a nucleus

  1. Nuclear fission is the splitting of a large, heavy nucleus into two smaller nuclei.
  2. In a nuclear power station the nucleus that splits is usually uranium-235. It absorbs a neutron, becomes unstable and splits into two smaller nuclei. It also releases neutrons, usually two or three, and energy.
  3. One possible fission of uranium-235 gives barium and krypton:
    92235U+01n→56144Ba+3689Kr+301n+energy
    apparatus diagram — not drawn yet

    Left to right: a single neutron moving towards a uranium-235 nucleus; then the nucleus splitting into two smaller nuclei labelled barium-144 and krypton-89 moving apart, with three neutrons flying out in different directions and a label 'energy released'.

    One neutron in; two smaller nuclei and three neutrons out. Count the nucleons on each side: 235 + 1 = 236 and 144 + 89 + 3 = 236.
  4. Every nuclide equation obeys two rules. The top numbers add up to the same total on both sides, because the number of nucleons does not change. The bottom numbers add up to the same total on both sides, because charge is not created or destroyed.
  5. Check the equation above. Top: 235+1=236 on the left and 144+89+3=236 on the right. Bottom: 92+0=92 on the left and 56+36+0=92 on the right. Both totals match, so the equation balances.
  6. The 3 in front of 01n means three neutrons. They add 3×1=3 to the top total and 3×0=0 to the bottom total. Multiply before you add.
  7. The trap here is to leave out the neutron on the left. The neutron that the uranium nucleus absorbs is part of the reaction, so its 1 and its 0 belong in the left-hand totals.
  8. To find a missing number, use the rule for its row. A missing top number comes from the top totals; a missing bottom number comes from the bottom totals. Never mix the two rows.

Part 7 of 8

Nuclear fusion: joining nuclei

  1. Nuclear fusion is the joining of two light nuclei to form one heavier nucleus.
  2. Fusion is the energy source of the Sun, where hydrogen nuclei join to make helium.
  3. One fusion reaction joins the two hydrogen isotopes hydrogen-2 and hydrogen-3 to make helium-4 and a neutron:
    12H+13H→24He+01n+energy
  4. The same two rules apply. Top: 2+3=5 on the left and 4+1=5 on the right. Bottom: 1+1=2 on the left and 2+0=2 on the right.
  5. Fusion is hard to make happen. Both nuclei are positively charged, so they repel each other. Only at extremely high temperatures do they move fast enough to get close enough to join.
  6. To tell the two processes apart from an equation, count the nuclei. One heavy nucleus (with a neutron) on the left and two smaller nuclei on the right is fission. Two light nuclei on the left and one heavier nucleus on the right is fusion.
  7. The words help too. A fissure is a split, as in a crack in rock; things that fuse are joined together.

Part 8 of 8

Mass and energy in fission and fusion

  1. Both fission and fusion release energy. This section is about where that energy comes from.
  2. Add up the masses of all the particles before the reaction, then the masses of all the particles after it. In both fission and fusion, the total mass after is slightly less than the total mass before.
  3. The mass that has gone has been converted into energy, and that is the energy released. Most of it is carried away as kinetic energy of the particles produced.
  4. This looks like it contradicts the balanced equation, but it does not. The top numbers balance because the number of nucleons is the same before and after. The mass can still fall, because the relative mass of a nucleus is only approximately equal to A: the products have the same number of nucleons but very slightly less mass in total.
  5. The objective says 'without values'. You describe the changes in words: the total mass decreases, and energy is released. You are not asked to calculate either one.
  6. So a complete description of either process has three parts: what happens to the nuclei (one heavy nucleus splits, or two light nuclei join), that the total mass of the products is less than the total mass before, and that energy is released.

Worked examples

Example 1. A nucleus of iron is represented as 2656Fe. Determine the number of protons and the number of neutrons in the nucleus, the number of electrons in a neutral atom of this isotope, and the relative charge and relative mass of the nucleus.

Show the working
  1. Read the two numbers from the symbol. The bottom number is the proton number, so Z=26: there are 26 protons. The top number is the nucleon number, so A=56.
  2. The neutrons are the nucleons that are not protons, so subtract.
    N=A−Z=56−26=30
  3. A neutral atom has as many electrons as protons, so it has 26 electrons. They are outside the nucleus, so they do not appear in either number.
  4. The relative charge on the nucleus comes from the 26 protons only, because the 30 neutrons are uncharged. So the relative charge is +26.
  5. Each of the 56 nucleons has a relative mass of about 1, so the relative mass of the nucleus is approximately 56.

Answer: 26 protons and 30 neutrons; 26 electrons in a neutral atom; relative charge on the nucleus +26; relative mass approximately 56.

Example 2. Four nuclides are labelled J, L, M and Q: 1735J, 1737L, 1837M and 1840Q. Identify which nuclides are isotopes of the same element. Explain your answer.

Show the working
  1. Isotopes must be the same element, so compare the bottom numbers first. J and L have Z=17. M and Q have Z=18.
  2. Within each pair, check that the neutron numbers differ. J: 35−17=18 neutrons. L: 37−17=20 neutrons. M: 37−18=19 neutrons. Q: 40−18=22 neutrons.
  3. So J and L are isotopes of one element: same number of protons (17), different numbers of neutrons (18 and 20). M and Q are isotopes of another element: 18 protons, with 19 and 22 neutrons.
  4. Now the trap. L and M have the same nucleon number, 37. They are still not isotopes, because they have different numbers of protons, so they are different elements.

Answer: J and L are isotopes of one element (both 17 protons; 18 and 20 neutrons). M and Q are isotopes of another element (both 18 protons; 19 and 22 neutrons). L and M share a nucleon number but have different proton numbers, so they are not isotopes.

Example 3. A uranium-235 nucleus absorbs a neutron and the reaction 92235U+01n→3890Sr+baXe+201n takes place. Determine the values of a and b, and describe the change in mass and the energy change in this reaction.

Show the working
  1. a is a top number, so use the top totals. Left: 235+1=236. Right: 90+a+2×1=92+a.
  2. Set the totals equal and solve.
    236=92+a⇒a=144
  3. b is a bottom number, so use the bottom totals. Left: 92+0=92. Right: 38+b+2×0=38+b.
  4. Set the totals equal and solve.
    92=38+b⇒b=54
  5. Now the description. A heavy nucleus has split into two smaller nuclei, so this is fission. The total mass of the strontium nucleus, the xenon nucleus and the two neutrons is slightly less than the total mass of the uranium nucleus and the neutron it absorbed.
  6. That decrease in mass has been converted into energy, which is released. No value is needed: the description in words is what the objective asks for.

Answer: a=144 and b=54. The total mass of the products is slightly less than the total mass of the uranium-235 nucleus and the neutron; the mass lost is converted into energy, which is released.

Example 4. Two hydrogen-2 nuclei join: 12H+12H→23He+particle Y. Deduce the nucleon number and the proton number of particle Y, and name it. State which process this is.

Show the working
  1. Top totals. Left: 2+2=4. Right: 3+(top number of Y). So the top number of Y is 4−3=1.
  2. Bottom totals. Left: 1+1=2. Right: 2+(bottom number of Y). So the bottom number of Y is 2−2=0.
  3. A particle with one nucleon and no charge is a neutron, 01n.
  4. Two light nuclei have joined to form one heavier nucleus, so this is fusion. Notice that both nuclei on the left are hydrogen: they have proton number 1, and they are the isotope hydrogen-2.

Answer: Y has nucleon number 1 and proton number 0: it is a neutron, 01n. The process is nuclear fusion.

Where people go wrong

Mistake: Reading the nucleon number A as the number of neutrons.

Instead: A is the number of protons plus neutrons. The number of neutrons is A−Z.

The top number counts every nucleon. 1123Na has 12 neutrons, not 23.

Mistake: Saying isotopes have different numbers of protons, or different numbers of electrons.

Instead: Isotopes have the same number of protons and different numbers of neutrons.

A different number of protons makes a different element. A different number of electrons makes an ion, which is a change outside the nucleus, not inside it.

Mistake: Saying the relative charge on a nucleus equals its nucleon number.

Instead: The relative charge on a nucleus equals its proton number, +Z.

Neutrons have zero charge, so only the protons contribute. It is the relative mass that is approximately A.

Mistake: Saying mass is conserved in fission or fusion because the top numbers in the equation balance.

Instead: The number of nucleons is conserved. The total mass after the reaction is slightly less than before, and the mass lost is released as energy.

The relative mass of a nucleus is only approximately equal to A. The top numbers count particles; they are not exact masses.

Mistake: Swapping the names: calling the splitting process fusion, or the joining process fission.

Instead: Fission is splitting a heavy nucleus. Fusion is joining two light nuclei.

A fissure is a split; things that fuse are joined. With the names swapped, every statement you make describes the other process.

Check yourself

  1. State the relative charges of a proton, a neutron and an electron.
    AnswerProton +1, neutron 0, electron −1.
  2. Describe the composition of a 24He nucleus.
    AnswerIt contains 2 protons and 2 neutrons: 4 nucleons in total. There are no electrons in the nucleus.
  3. A sodium nucleus has proton number 11 and nucleon number 23. Calculate the number of neutrons in it.
    AnswerN=A−Z=23−11=12 neutrons.
  4. A nucleus of oxygen (symbol O) has 8 protons and 9 neutrons. Give it in nuclide notation.
    AnswerA=8+9=17 and Z=8, so 817O.
  5. Carbon has proton number 6. Explain why carbon-12 and carbon-14 are isotopes.
    AnswerBoth have 6 protons, so they are the same element. Carbon-12 has 12−6=6 neutrons and carbon-14 has 14−6=8 neutrons, so they have different numbers of neutrons.
  6. State the relative charge and the relative mass of a 92238U nucleus.
    AnswerRelative charge +92 (equal to the proton number); relative mass approximately 238 (approximately equal to the nucleon number).
  7. Find the missing nucleon number in 92235U+01n→54140Xe+38?Sr+201n.
    AnswerTop totals: 235+1=236, and 140+?+2=236, so the missing number is 94.
  8. In nuclear fusion, how does the total mass of the products compare with the total mass before the reaction, and what is released?
    AnswerThe total mass of the products is slightly less. The mass lost is converted into energy, which is released.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. A nucleus of one isotope of oxygen is represented as 818O.

(a) State the number of protons and the number of neutrons in this nucleus. 2 marks No calculator

Mark scheme
  • B1 8 protons
  • B1 10 neutrons

(b) Define the term nucleon number. 1 mark No calculator

Mark scheme
  • B1 the (total) number of protons and neutrons in a nucleus; 'number of nucleons' alone is insufficient

(c) A different isotope of oxygen has 8 neutrons in its nucleus. Give the nuclide notation for a nucleus of this isotope. 1 mark No calculator

Mark scheme
  • B1 16 at the top and 8 at the bottom of the symbol O, i.e. 816O

(d) Explain, in terms of the particles in their nuclei, why the nucleus in the stem and the nucleus in (c) are isotopes of the same element. 2 marks No calculator

Mark scheme
  • B1 same number of protons / same proton number (8)
  • B1 different numbers of neutrons (10 and 8) / different nucleon numbers

(e) Compare the relative charge and the relative mass of the nucleus in the stem with those of the nucleus in (c). 2 marks No calculator

Mark scheme
  • B1 same relative charge, +8, for both
  • B1 relative masses (approximately) 18 and 16, so the nucleus in the stem is heavier / has the greater mass, owtte; ecf from (c)

Question 2. In a nuclear reactor, a nucleus of uranium-235 absorbs a neutron. The reaction is 92235U+01n→56141Ba+36xKr+301n.

(a) Identify the type of nuclear reaction shown by the equation. 1 mark No calculator

Mark scheme
  • B1 (nuclear) fission

(b) Calculate the value of x. 2 marks No calculator

Mark scheme
  • C1 235 + 1 = 141 + x + 3, or nucleon numbers on the two sides equated
  • A1 92

(c) Describe the change in mass and the energy change that take place in this reaction. 2 marks No calculator

Mark scheme
  • B1 total mass of the products (Ba, Kr and the three neutrons) is less than the total mass of the uranium nucleus and the neutron / (total) mass decreases, owtte
  • B1 energy is released / the mass lost is converted into energy, owtte; ignore any numerical values

Question 3. In an experimental fusion reactor, nuclei of two isotopes of hydrogen, hydrogen-2 and hydrogen-3, are made to join. The reaction is 12H+13H→24He+Y.

(a) Deduce the nucleon number and the proton number of particle Y, and name particle Y. 2 marks No calculator

Mark scheme
  • B1 nucleon number 1 and proton number 0
  • B1 neutron

(b) Explain, in terms of protons and neutrons, why a hydrogen-3 nucleus has a greater mass than a hydrogen-2 nucleus but the same charge. 2 marks No calculator

Mark scheme
  • B1 both nuclei have one proton (neutrons are uncharged), so both have relative charge +1
  • B1 hydrogen-3 has two neutrons and hydrogen-2 has one, so hydrogen-3 has more nucleons (3 against 2) and so a greater mass

(c) Compare nuclear fusion with nuclear fission. 3 marks No calculator

Mark scheme
  • B1 fusion: two light / small nuclei join to form a heavier nucleus
  • B1 fission: a heavy / large nucleus splits into (two) smaller nuclei
  • B1 similarity: both release energy / in both the total mass of the products is less than the total mass before

How this is examined

  • Describing fission and fusion, with the mass and energy changes: a two- or three-mark Describe or Compare part, which may sit after a nuclide equation for one of the two processes What happens to the nuclei: fission — a heavy (large) nucleus splits into two smaller nuclei; fusion — two light (small) nuclei join to form a heavier nucleus. Then the mass and energy changes in words: the total mass of the products is less than the total mass before, and energy is released. No numerical values are needed.
  • Balancing a nuclide equation to find a missing number or particle: a one- or two-mark Calculate or Deduce part, or an equation to complete, on a fission or fusion equation with one number or one particle missing Top numbers totalled on both sides and set equal for a missing nucleon number; bottom numbers totalled and set equal for a missing proton number. Neutrons counted with their multiplier and the absorbed neutron included on the left. For a missing particle, both numbers and its name: 1 and 0 is a neutron.
  • Saying what an isotope is: a two-mark Explain part about two given nuclides of the same element Both halves: the same number of protons (same proton number), and a different number of neutrons (different nucleon number). Quoting the actual numbers from the nuclides makes each point specific.
  • Counting the particles in a nucleus from nuclide notation: one- or two-mark State or Calculate parts on a given symbol such as ZAX Protons = bottom number Z; neutrons = A−Z; electrons in a neutral atom = Z. In the other direction, a symbol with A = protons + neutrons on top and Z = protons below.
  • Defining proton number and nucleon number: one-mark Define parts Proton number: the number of protons in the nucleus. Nucleon number: the number of protons and neutrons in the nucleus. 'The number of nucleons' only restates the term, so say what a nucleon is.
  • Relative charges of the particles, and the charge and mass of a nucleus: one-mark State parts Proton +1, neutron 0, electron −1. The relative charge on a nucleus is +Z; its relative mass is approximately A. Isotopes: same charge on the nucleus, different mass.

Words to know

Nucleus
The very small, positively charged centre of an atom, made of protons and neutrons.
Proton
A particle in the nucleus with relative charge +1 and relative mass 1.
Neutron
A particle in the nucleus with relative charge 0 and relative mass 1.
Electron
A particle that orbits outside the nucleus, with relative charge −1 and a mass about 11840 of a proton's.
Nucleon
Any particle in the nucleus: a proton or a neutron.
Proton number (atomic number), Z
The number of protons in the nucleus. It decides the element, and it equals the relative charge on the nucleus.
Nucleon number (mass number), A
The number of protons and neutrons in the nucleus. The relative mass of the nucleus is approximately equal to it.
Nuclide notation
The symbol ZAX, with the nucleon number at the top left and the proton number at the bottom left of the element's symbol.
Isotopes
Atoms of the same element with the same number of protons and different numbers of neutrons.
Nuclear fission
The splitting of a heavy nucleus into two smaller nuclei, with a decrease in total mass and the release of energy.
Nuclear fusion
The joining of two light nuclei to form a heavier nucleus, with a decrease in total mass and the release of energy.