• The important point to realise right from the start is that radioactivity occurs when the UNSTABLE NUCLEUS of an atom undergoes a fundamental change (disintegration) that results in a different nucleus (of an atom) being formed and accompanied by the emission of alpha particles or beta particles or gamma radiation.

• The nucleus is composed of protons and neutrons and glued together by a strong nuclear attractive forces BUT only certain combinations of the neutron/proton (n/p) ratio in the nucleus seem to be more stable than others.
  • See graphs in Isotope stability curve graph related to modes of radioactive decay
• Any isotope of any element that does not lie in the stability band with a stable n/p ratio is more likely to be radioactive!
• Radioactivity results from the random and spontaneous breakdown of the unstable nucleus of an atom.
• ALSO, remember that isotopes are atoms of the same atomic number (same element) but different mass numbers.
  • Some elements have just a few isotopes but others may have up to many different isotopes.
  • Most elements have a few stable isotopes, but many other isotopes are unstable, when the nucleus disintegrates spontaneously (radioactive decay) and these atoms (isotopes) are described as radioactive, emitting ionising (nuclear) radiation e.g. alpha, beta and gamma radiation in the process.
  • As well these ionising radiation emissions, neutrons can also be released and ALL these emissions are to do with nuclear instability when an unstable nucleus changes to a more stable nucleus.

• Read atomic symbols of any isotope e.g. an isotope of sodium, 11 protons, 12 neutrons, mass 23

  • Top left number is the nucleon number or mass number (A = sum of protons + neutrons = nucleons)

  • Bottom left number is the atomic number or proton number (Z = protons in nucleus)

  • The neutron number N = A – Z i.e. mass/nucleon number – atomic/proton number

  • Therefore from the following 'full' atomic symbols, assuming we are dealing with electrically neutral atoms, the number of sub-atomic particles for the following atoms will be as follows ...

  • Cobalt atom (isotope cobalt–59), mass 59, 27 protons, 32 neutrons (59 – 27)

  • Californium atom (isotope californium–246), mass 246, 98 protons, 148 neutrons (246 – 98)

AND balancing nuclear equations

(1) The emission of an alpha particle or beta particle leads to a change in the composition of a nucleus in terms of protons or neutrons.

The emission of a gamma photon does NOT change the composition of the nucleus, it only lowers the energy associated with the nucleus after the radioactive decay has taken place.

Gamma radiation often accompanies radioactive decay by alpha particle or beta particle emission.

(2) The mode of radioactive decay (emission), i.e. alpha (helium nucleus), beta minus (electron) and beta plus (positron), or not at all for a stable nucleus, strongly depends on the neutron/proton ratio, how high the atomic number is and the energy state of the nucleus.

The nucleus for a specific element (specific atomic/proton number) may be unstable due to ....

(i) too many neutrons, too high a neutron/proton ratio, tend to decay by beta minus (electron) emission to reduce the neutron/proton ratio.

(ii) too few neutrons, too low a neutron/proton ratio, tend to decay by positron (+ electron) emission to increase the neutron/proton ration.

(iii) too high a total of protons and neutrons, tend to decay by alpha emission with elements of Z > 82 (Pb) - all very large nuclei seem to be unstable and disintegrate by radioactive decay.

(iv) After a radioactive decay has taken place producing a new nucleus, the new nucleus may highly unstable and have excess energy, and so it loses energy as gamma radiation to attain its more stable nuclear state.

7c. Stable and unstable isotopes - the stability curve

When you plot the number of neutrons (N) versus the number of protons (Z) you a slightly curved band of stable isotopes for most elements from Z = 1 to Z = 92. Any isotope lying above or below this stable band will tend to be unstable i.e. radioactive.

Because of all the nuclear changes that are possible it means that it is almost impossible to have a 'pure' radioisotope of any element.

See APPENDIX 1 for detailed data graphs to elaborate on the crude little graph above right, which illustrate (i) to (iii)

The changes due to radioactivity can be represented as nuclear equations and they must balance in mass and charge i.e. what ever the nature of the initial isotopes, for the new isotopes formed and the particles emitted, both the total mass and electric charge must remain the same, that is mass and charge are conserved.

Radioactive decay equations are usually of the form:

parent atom before decay ==> daughter atom after decay + emitted radiation-particle

and other equations might be of the form:

two parent atoms or particles ==> two daughter atoms or particles

For ANY nuclear equation to balance - for both sides:

(a) The atomic numbers must add up to the same value on each side of the equation.

(These are the lower bottom-left numbers on the symbol for the atom or particle).

However, this rule also equates to conservation of electric charge.

If the decay equation (or any other) involves a beta particle (negative electron) or a positron (positive electron), you must add these up with the positive proton numbers.

(b) The mass numbers on either side of a nuclear equation must add up to the same value.

(These are the higher top-left numbers on the symbol for the atom or particle).

This is not usually a problem to work out most equations., but watch out for beta particles or positrons counting as zero mass (1/1860 doesn't count in these deductions, taken as ~0, as is the mass of the gamma photon - electromagnetic radiation).

Examples - with complete explanations given as you work your way down the page.

Examples of word and symbol equations for nuclear reactions

Note in word equations the mass number of the isotope is quoted with a dash after the elements name.

(i) cobalt-60 ====> nickel-60  +  beta particle

  (beta particle emission)

total mass 60, total charge 27+ (28 - 1)

(ii) magnesium-23  ====>  sodium-23  +  positron

   (positron emission)

total mass 23, total charge 12+ (11 + 1)

(iii) radium-223  ====> radon-219  +  alpha particle

 (alpha particle emission)

total mass 223 (219+4), total charge 88+ (86 + 2)

(iv) uranium-235  + neutron ===>  lanthanum-145  +  bromine-88  +  three neutrons

 

(nuclear fission, a bit more tricky to balance!)

total mass 235 (145 + 88 + 3), total charge 92 (57 + 35)

If you can follow these examples now, most of the rest of the page should prove quite easy to follow!

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7e. ALPHA DECAY  equations: Alpha particle emission, helium nucleus emitted

• Alpha Decay e.g. a nuclear equation radioactive decay emitting an alpha particle, usually from heavy nuclei

  • (i) uranium-235  ===> thorium-231  +  alpha particle

    •  

    • 

  • Uranium-235 is converted into thorium-90 with alpha particle and gamma photon emission

  • In alpha decay a helium nucleus, the alpha particle, of 2 protons and 2 neutrons is emitted at high speed/kinetic energy from the nucleus.

  • The residual atom, often referred to as the politically incorrect 'daughter nuclide', has a mass number of 4 less, and an atomic number of 2 less, compared to the 'parent' or original atom.

    • Sadly, apart from both Nobel Prize winning Marie Curie and her daughter (Irène Joliot-Curie), in the late 19thC/early 20thC, nuclear physics was dominated by male scientists!

  • Note that the total mass numbers on each side of the equation must be equal to balance and similarly the atomic number totals must also be the same on each side of the nuclear equation to complete the balance.

  • How to balance the mass and charge for alpha decay equations:

    • For alpha emission balancing for (i) total mass = 235 = 231 + 4 and protons = 92 = 90 + 2

    • Note the protons are positive so the 92 = 90 + 2 = conservation of electric charge.

  • Sometimes gamma radiation is also emitted, if so, it doesn't affect the balancing of the nuclear equation because a gamma photon has zero mass and zero charge.

  • All 'heavy' atoms with an proton/atomic number of Z over 82 (Pb) have isotopes that undergo alpha decay.

    • See PLOT (3) in APPENDIX 1, where you will also see that many heavy isotopes also undergo beta decay too.

  • Other examples of nuclear equations for alpha decay
    • (ii) radium-223  ====> radon-219  + alpha particle
      •  
      • 
      • radium-223 is converted to radon-219 with alpha particle and gamma photon emission
      • mass balance: 223 = 219 + 4 + 0
      • conservation of charge: 88 = 86 + 2 + 0
    • (iii) americium-243  ====>   neptunium-239  +  alpha particle
      • 
      • 
      • americium-243 is converted into neptunium-239 with alpha particle and gamma emission
      • mass balance: 243 = 239 + 4 + 0
      • conservation of charge: 95 = 93 + 2 + 0
      • Note on gamma emission:
        • When the new nucleus is formed, it can be in a highly energised (excited) state.
        • To become stable, it loses the excess energy by the extra emission of a gamma photon.
        • The emission of the gamma radiation might not be shown in the equation, and sometimes it is actually shown by a secondary equation e.g. for the last nuclear equation above
        • 
  • In each case the mass number (nucleon number) drops by 4 and the atomic/proton number decreases by two to give a different element.
  • In all cases of alpha particle emission from an unstable nucleus a new element is formed i.e. the 'transmutation' of one element to another has happened.
  • more on properties of alpha particles & uses of alpha radiation

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• Beta minus decay (electron emission) e.g. a nuclear equation to illustrate radioactive decay by beta particle emission

  • (i) carbon-14  ====>  nitrogen-14  +  beta minus particle

    •  

  • Carbon-14 is converted into nitrogen-14 with beta particle emission.

  • The neutron/proton ratio changes from 8/6 to 7/7 (1.3 to 1.0).

  • In beta minus decay a neutron in the nucleus changes spontaneously into a proton and a high kinetic energy electron forms the emitted beta minus particle.

  • Note to be balanced, the total mass remains constant and in this case to completely balance the equation, the electric charge must balance i.e. +6 (protons) = +7 (protons) + -1 (electron)

  • Since the proton and neutron have a mass of 1 and the electrons mass is negligible, the mass number stays the same but the atomic (proton) number rises by 1.

  • How to balance the mass and charge for beta minus decay equations:

    • For beta minus emission balancing (i) mass = 14 = 14 + 0 and for protons/beta minus charge = 6 = 7 + (-1).

    • Remember to think of the number of protons as the number of positive charges.

      • So the 6 = 7 - 1 = conservation of electric charge.

  • Beta minus decay tends to happen with isotopes with too many neutrons to be stable (too high an n/p ratio) and lies above the stability curve shown above and now better shown in APPENDIX 1 PLOTS (1) and (2).

  • By changing a neutron to a proton the n/p ratio is reduced to the nucleus of an isotope lying in the stability band.

  • Other examples of nuclear equations for beta decay
    • (ii) cobalt-60  ====>  nickel-60  +  beta minus particle
      •    
      •  
      • cobalt-60 is converted into nickel-60 with beta particle and gamma photon emission
        • mass balance: 60 = 60 + 0
        • charge balance: 27 = 28 -1
    • (iii) radium-228  ====>  actinium-89  + beta minus particle
      • 
      • radium-228 is converted into actinium-228 with beta particle emission
        • mass balance: 228 = 228 + 0
        • charge balance: 88 = 89 -1
    • (iv) iodine-131  ====>  xenon-131  +  beta minus particle
      • 
      •  
      • the iodine-131 nucleus changes to a xenon nucleus with the emission of a beta particle and gamma photon.
        • mass balance 131 = 131 + 0
        • charge balance: 53 = 54 -1
    • (v) sodium-24  ===>  magnesium-24  +  beta minus particle
      •  
      • 
      • sodium-24 changes to the isotope magnesium-24 with emission of beta particle and a gamma photon.
        • mass balance: 24 = 24 + 0
        • charge balance: 11 = 12 -1
  • For beta minus decay, in each case the mass number (nucleon number) stays the same but the atomic/proton number increases by one to give a different element.
  • In all cases of an beta minus particle emission from an unstable nucleus a new element is formed i.e. the 'transmutation' of one element to another has happened.
• more on properties of beta particles & uses of beta radiation
• For quarks and advanced theory of beta minus decay see APPENDIX 2

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• Gamma emission: Emission of gamma radiation from a nucleus does NOT involve any change in the atomic (proton) number or mass (nucleon) number i.e. no change in the particle composition of the nucleus.

  • When a 'new' nucleus is formed it tends to have excess energy making it potentially unstable.

  • To become more 'nuclear stable' the nucleus loses some energy as a burst of gamma radiation (a gamma photon) but the proton and neutron numbers do not change.

  • This is a decrease in the nuclear energy store change to form electromagnetic radiation - which would ultimately end up increasing the thermal energy store of the surroundings on absorption, but not before ionising molecules and promoting chemical changes.

  • This can be observed with both alpha particle or beta particle emission e.g.

  • (alpha)  uranium-235  ===> thorium-231  +  alpha particle

    •    (without showing gamma emission)

    •    (showing gamma emission)

    • 231 90

      Th

      231 90

      Th

    • Just showing the secondary effect - the gamma photon emission - no change in atomic/mass numbers!
  • (beta)  cobalt-60  ===>  nickel-60  +  beta minus particle
    •      (without showing gamma emission)
    •     (showing gamma emission)

    • 60 28

      Ni

      60 28

      Ni

    • Just showing the secondary effect - the gamma photon emission - no change in atomic/mass numbers.
  • more on properties of gamma radiation & uses of gamma radiation

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• Positron emission (beta plus decay) e.g. a nuclear equation to illustrate radioactive decay by positron emission

  • e.g. (i)  magnesium-23  ===>  sodium-23  +  positron (beta plus particle)

    •  

    •  

    • and then    e⁺ + e^–   ==> 2   

    • annihilation with the nearest available electron, so positrons don't get very far!

    • Note the conservation of electric charge i.e. (+) + (–) = 0 (gamma photons are electrically neutral), but the mass isn't conserved, but energy is, because the two particles are converted into two gamma photons, that is electromagnetic radiation energy (a case of E = mc² !).

    • A positron is a positive electron and the antiparticle of the more familiar negative electron.

    • • A pair of antiparticles have the same mass but opposite electric charges.

    • Positron emitting radioisotopes are effectively gamma photon emitters because the positrons don't get very far due to their almost immediate annihilation.

    • These short-lived isotopes are used in medical physics techniques like PET scanning.

  • Magnesium-23 changes to sodium-23 with emission of positron (positive electron)

  • The neutron/proton ratio changes from11/12 to 12/11 (0.92 to 1.1).

  • In positron emission (beta plus decay), a proton changes to a neutron  and  a 'positive electron' called a positron is expelled with very high kinetic energy.

  • A positron has the same mass as an electron but carries a positive charge (it is the 'anti-matter' particle of the electron!).

  • Since the proton and neutron have a mass of 1 and the electrons mass is negligible, the mass number stays the same but the atomic (proton) number falls by 1.

  • How to balance the mass and charge for beta plus decay equations:

    • For beta plus emission balancing (i) mass = 23 = 23 + 0 and for protons/beta plus charge = 12 = 11 + (+1).

    • Remember to think of the number of protons as the number of positive charges.

      • So the 12 = 11 + 1 = conservation of electric charge.

  • Beta plus decay tends to happen with isotopes with too few neutrons to be stable (too low an n/p ratio) and lies below the stability curve shown in the graph above and now better shown in APPENDIX 1 PLOTS (1) and (2).

  • By changing a proton to a neutron the n/p ratio is increased to an isotope lying in the nuclear stability band.

  • Other examples of nuclear equations for beta plus decay
    • (ii) to (iv) These three isotopes are used in PET scanning which uses positron emitters.
    • (ii)  fluorine-18  ===>  oxygen-18  +  positron (beta plus particle)

      18 9

      F

      18 8

      O

      +

      0 +1

      e

      • fluorine-18 decays to oxygen-18 plus a positron
      • mass balance: 18 = 18 + 0
      • charge balance: 9 = 8 +1
        • fluorine-18 is made by bombarding oxygen-18 with protons in a cyclotron.
    • (iii) carbon-11  ====>  boron-11  +  positron (beta plus particle)

      11 6

      C

      11 5

      B

      +

      0 1

      e

      • carbon-11 decays to boron-11 plus a positron
      • mass balance: 11 = 11 + 0
      • charge balance: 6 = 5 +1
        • carbon-11 is made by bombarding nitrogen atoms with protons in a cyclotron.
    • (iv)  nitrogen-13  ====>  carbon-13  +  positron (beta plus particle)

      13 7

      N

      13 6

      C

      +

      0 +1

      e

      • nitrogen-13 decays to carbon-13 plus a positron
      • mass balance: 13 = 13 + 0
      • charge balance: 7 = 6 +1
        • nitrogen-13 is made by bombarding oxygen atoms with protons in a cyclotron.
  • For positron emission (beta plus decay), in each case the mass number (nucleon number) stays the same but the atomic/proton number decreases by one to give a different element (the latter is the opposite of beta decay).
  • In all cases of an beta plus particle emission from an unstable nucleus a new element is formed i.e. the 'transmutation' of one element to another has happened.
  • For quarks and advanced theory of beta plus decay see APPENDIX 2 (NOT for GCSE students).

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This is a relatively less common nuclear change, but it can happen with very unstable atoms with a very high neutron to proton ratio in the nucleus (n/p).

The atomic number remains the same, so element does not change identity.

However, the mass number and neutron numbers will fall by one unit.

e.g. boron-13 (n/p= 8/5) changing to boron-12 (n/p = 7/5) with the emission of a neutron.

boron-13  ===>  boron-12  +  neutron

13 5

B

12 5

B

+

1 0

n

mass balance: 13 = 12 + 1;  charge balance: 5 = 5

The half-life of boron-13 is 0.02 seconds - not very stable.

By losing a neutron, the neutron/proton is decreased tending to produce a more stable nucleus.

However in this case, boron-12 still has a too high a neutron/proton ratio and by coincidence also has a half-life of ~0.02 seconds.

Many of the lighter elements have a neutron/proton ratio of 1 and boron-12 actually decays by beta minus (-) particle emission to form a very stable carbon-12 atom with a neutron/proton ratio of 1.

boron-12  ===>  carbon-12  +  beta minus particle

12 5

B

12 6

C

+

0 -1

e

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• NUCLEAR FISSION equations - not radioactive decay, but big nuclei splitting into smaller nuclei e.g.

  • uranium-235  + neutron  ===>   lanthanum-145  +  bromine-88  +  three neutrons

  • 

    • mass balance: 235 + 1 = 236 = 145 + 88 + 3

    • charge balance: 92 + 0 = 92 = 57 + 35

    • -

  • uranium-235  +  neutron  ===>  molybdenum-95  +  lanthanum-139  + two neutrons + seven beta minus particles

  • 

    • mass balance: 235 + 1 = 236 = 95 + 139 + 2 + 0

    • charge balance: 92 + 0 = 92 = 42 + 57 +0  -7

    • -

  • Fission is when an atomic nucleus splits into two smaller nuclei - accompanied by the production of neutrons and electrons.

  • They can be quite complicated and lots of smaller nuclei are formed, I've just picked out equations showing the formation of several possibilities.

  • Check the balancing for yourself - simple arithmetic, but take care! but all the top mass numbers should add up to be equal on both sides of the equation, similarly for all the atomic (positive charge) numbers.

  • For more see section 9. Nuclear Fission

• NUCLEAR FUSION equations - not radioactive decay, but fusing two smaller nuclei into a bigger nucleus e.g.

  • hydrogen-1  +  hydrogen-2  ===>  helium-3

  • 

  • mass balance:  1 + 2 = 3; charge balance: 1 + 1 = 2

  • -

  • carbon-13  +  helium-4  ===>  oxygen-16  +  neutron

  • 

    • mass balance:  13 + 4 = 17 = 16 + 1; charge balance: 6 + 2 = 8 + 0

    • -

  • nitrogen-14  +  helium-4  ===>  fluorine-17  +  neutron

  • 

    • mass balance:  14 + 4 = 18 = 17 + 1; charge balance: 7 + 2 = 9 + 0

    • -

  • The next three show how you can synthesise transuranium elements (Z > 92)

  • uranium-238  +  nitrogen-14  ===>  einsteinium-248  +  four neutrons

  •  m

    • mass balance:  238 + 14 = 252 = 248 + 4; charge balance: 92 + 7 = 99 + 0

    • -

  • uranium-238  +  carbon-12  ===>  californium-246  +  four neutrons

  •  

    • mass balance: 238 + 12 = 250 = 246 + 4; charge balance: 92 + 6 = 98 + 0

  • californium-252  + boron-11  ===>  lawrencium-257  +  six neutrons

  •  

    • mass balance: 252 + 11 = 263 = 257 + 6; charge balance: 98 + 5 = 103

  • Fusion is the process by which two smaller nuclei are fused into a larger nucleus - often smaller particles like a neutrons are also produced in the process

  • You find these are balanced in exactly the same way as for radioactive decay, check out the numbers for your self.

  • All the mass numbers should be equal on each side of the equations and note the need for balancing numbers like in chemical equations, except these are nuclear equations!

  • The lower numbers must add up to on both sides of the equation, that is the electric charge must balance (proton positive or minus for electron).

  • For more see section 8. Nuclear Fusion

7k. The production of radioisotopes - how to make artificial sources of radioactivity by bombarding atoms with neutrons

• The USES of RADIOISOTOPES are fully described in section 5.

• Neutron bombardment is a common method used to make artificial or man-made radioisotopes.

  • I remember as a student in 1967 visiting a research reactor at Risley near Manchester, England. A round the nuclear reactor where a circular band of well protected laboratories enabled samples to be inserted into the reactor core. After neutron bombardment in the reactor, the sample could be withdrawn into special fume cupboards and processed in a safe way to extract and purify the desired product.

• To meet the industrial and medical demand for radioactive-isotopes (as described earlier) many are made by allowing stable isotopes to be hit by neutrons in a small research scale nuclear reactor to make unstable, but useful radioisotopes.

• Note again, the balancing of nuclear equations to illustrate the production of radioactive-isotopes e.g.

• Check out the mass and charge balances for yourself - these are all quite easy.

• (a) oxygen-16  +  neutron  ===>  carbon-13  +  helium-4

  • 

  • Oxygen-16 atoms are bombarded with neutrons to make the radioisotope carbon-13, used as a chemical tracer carbon in studying the mechanisms in organic chemistry reactions, you can follow what happens to a particular carbon atom i.e. follow what happens to a particular part of a molecule.

  • -

• (b) sodium-23  +  neutron  ===>  sodium-24

  • 

  • Sodium-23 atoms are bombarded with neutrons to make the radioisotope sodium-24, which can be used in tracer studies of animal blood circulation, an important diagnostic tool in clinical medicine.

  • -

• (c) cobalt-59  + neutron  ===>  cobalt-60

  • 

  • Cobalt-59 atoms are bombarded with neutrons to make the radioisotope cobalt-60, used as the gamma source for cancer radiotherapy. The deadly gamma rays from the decay of the unstable cobalt-60 atoms are directed at cancer cells to kill them.

  • -

• (d) tellurium-130  +  neutron  ===> tellurium-131  ===>  iodine-131  +  beta minus particle

  • 

  • Tellurium-130 is irradiated ('bombarded') with neutrons to form the heavier isotope tellurium-131, which then undergoes beta decay to form iodine-131 used in medical tracer studies.

  • -

• Quite a lot of useful radioisotopes are obtained from the spent fuel rods from nuclear reactors.

• e.g. americium-241 (used in smoke alarms) is a decay product of plutonium-241 and when reprocessing nuclear fuel rods americium-241 along with many other radioisotopes can be separated by a complex chemical processing procedures. The original fuel may be uranium-238.

• uranium-238  == 5 steps ==>  plutonium-241  ===> americium-241  + beta minus particle

• 

• See APPENDIX 3 for the making of positron emitters (beta plus decay) in a CYCLOTRON by bombarding isotopes with protons.

• The USES of RADIOISOTOPES are fully described in section 5.

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APPENDIX 1

7l. ISOTOPE STABILITY CURVE GRAPH and MODES of RADIOACTIVE DECAY

Details NOT required for GCSE students! - just detailed graphical extensions of the general idea of a stability band related to modes of radioactive decay.

These graphs were produced using information from a data book dated 1980.

I've used almost every isotope that is stable or radioactive emitting alpha, beta minus (electron) and beta plus (positron) radiation.

Many are naturally occurring but I've included artificially produced radioisotopes.

I know there are plenty of other isotopes but the data was quite sufficient to show the patterns e.g. the stability bands and the other bands of region of unstable radioactive isotopes with their various decay modes.

(1) Plot of proton number (atomic number) versus neutrons in the isotopes of the elements 1 to 30

(the first point is a neutron with a half-life of 10 mins!).

(2) Plot of proton number (atomic number) versus neutrons in the isotopes of the elements 1 to 70.

Its only above atomic number (proton number) of ~57 you begin to see radioactive decay by emission of alpha particle.

(3) Plot of proton number (atomic number) versus neutrons in the isotopes of the elements 1 to 102.

You can see immediately that many isotopes of heavy atoms, particularly for Z >82 (Pb), now decay by alpha particle emission as opposed to just beta plus or beta minus decay.

Many radioisotopes of heavy atoms also decay by beta particle emission.

Although beta– decay sees the mass number staying the same and the atomic number is raised by 1, ultimately the heavy atoms well above Z = 83, decay via a complex series of changes to more stable isotopes of lead (Z = 82) because with alpha particle emission you lose 4 mass units and the atomic number reduces by 2 units.

This 'up and down' of the atomic number (Z) is illustrated below with part of the uranium-238 decay series which occurs naturally in the environment e.g. in rocks containing uranium minerals ...

²³⁸₉₂U =α=> ²³⁴₉₀Th =β=> ²³⁴₉₁Pa =β=> ²³⁴₉₂U =α=> ²³⁰₉₀Th =α=> ²²⁶₈₈Ra =α=> ²²²₈₆Rn =α=> ²¹⁸₈₄Po =α=>²¹⁴₈₂Pb

... and unstable lead-214 then decays by four beta decays and two alpha particle decays to stable lead-206 ...

²¹⁴₈₂Pb =β=> ²¹⁴₈₃Bi =β=> ²¹⁴₈₄Po =α= ²¹⁰₈₂Pb =β=> ²¹⁰₈₃Bi =β=>²¹⁰₈₄Po =α=> ²⁰⁶₈₂Pb  ... the half-lives of theses unstable nuclei range from a few minutes to a few million years, so the overall decay process takes many millions of years!

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7m. APPENDIX 2 RADIOACTIVE DECAY and QUARKS (NOT for GCSE students!)

• Quark changes and radioactive decay

  • Quarks and beta minus decay: emission

  • If an isotope has too many neutrons in the nucleus to be stable (too high a neutron/proton ratio) it undergoes beta– radioactive decay (β^– decay) to form a more stable nucleus.

    • The following changes occur in the unstable nucleus to make a more stable nucleus.

    • A neutron changes into a proton and an electron, the latter is expelled from the nucleus as a negative beta particle.

    • neutron ==> proton + electron (beta– particle)

      • Symbolically this can be expressed as ...

      •    (beta – decay)

      • Note that the total initial electrical charge (0) must be conserved, a fundamental law of physics.

        • From a neutral particle the +1 of the proton is balanced by the –1 of the electron.

    • In terms of quark changes, a down–quark changes to an up–quark in the [nucleus]

    • (neutron) ['up–quark + 'down–quark' + 'down–quark'] ==> ['up–quark' + 'up–quark' + 'down–quark'] (proton)

      • e.g. beta- decay: This happens when a molybdenum-98 nucleus decays by beta- particle emission to give an atom of technetium (higher atomic/proton number) and emission of a beta particle (negative electron).

      • 

    • –

  • Quarks and beta plus decay: emission

  • If an isotope has too many protons in the nucleus to be stable (too high a proton/neutron ratio) it undergoes beta+ radioactive decay (β⁺ decay) to form a more stable nucleus.

    • The following changes occur in the unstable nucleus to make a more stable nucleus.

    • A proton changes into a neutron and a positron (positive electron), the latter is expelled from the nucleus as a positive beta particle (negative electron).

    • proton ==> neutron + positron (beta+ particle)

      • Symbolically this can be expressed as ...

      •     (beta + decay)

      • Note that the total initial electrical charge (+1) must be conserved, a fundamental law of physics.

        • The original positive +1 proton particle produces +1 positron and a neutral particle.

    • In terms of quark changes, an up–quark changes to a down–quark in the [nucleus]

    • (proton) ['up–quark + 'up–quark' + 'down–quark'] ==> ['up–quark' + 'down–quark' + 'down–quark'] (neutron)

      • e.g. beta+ decay: This happens in the beta+ decay of an oxygen–15 nucleus by positron emission to give nitrogen–15 (lower atomic/proton number) and emission of a positron (positive electron)

      •  

    • –

  • For more notes about quarks see the radioactivity -atomic structure page

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7n. APPENDIX 3 Particle accelerators - the cyclotron for making radioisotopes

A cyclotron is a compact type of particle accelerator machine by which electrically charged particles (usually positive, often protons) are accelerated outwards from the centre along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated along circular paths by a rapidly varying (radio frequency) electric field.

The target stable non-radioactive isotope is placed in the cyclotron bombarded with a beam of accelerated smaller particle e.g. a proton (a hydrogen-1 nucleus), a process sometimes described as 'proton enrichment'. The protons must be accelerated to enormous speeds to have enough energy to be absorbed into another nucleus, thereby raising the atomic number by 1.

After the stable isotopes have reacted with the proton beam to form radioactive isotopes, these are then taken from the cyclotron,
and transformed into positron-emitting radiopharmaceuticals within the facility’s laboratories and are delivered to a nuclear medicine facility where they are used for PET imaging procedures.

Cyclotrons are a clean nuclear technology with very little radioactive waste.

Examples of producing positron emitters for PET scanning in medicine (see uses of radioisotopes)

The equations are easy to balance in terms of top left mass numbers and bottom left proton numbers (no complications due to electrons or positrons). The decay equations for (i) to (iii) emitting positrons are given in the beta plus section above.

Important note:

The positron emitting atoms must be incorporated into a suitable compound which can be injected into the patient.

e.g. oxygen in water (H₂O), carbon or oxygen in glucose (C₆H₁₂O₆), nitrogen in an amino acid H₂NCHRCOOH.

(i) fluorine-18   ¹⁸F, is made by bombarding oxygen-18 with protons

oxygen-18  +  proton  ===>  fluorine-18  +  neutron

18 8

O

+

1 1

H

18 9

F

+

1 0

n

The oxygen-18 is in water molecules enriched with oxygen-18 containing water molecules.

(ii) carbon-11   ¹¹C, is made by bombarding nitrogen atoms with protons

nitrogen-14  +  proton  ===>  carbon-11  +  helium-4

14 7

N

+

1 1

H

11 6

C

+

4 2

He

(iii) nitrogen-13   ¹³N, is made by bombarding oxygen atoms with protons

oxygen-18  +  proton  ===>  nitrogen-13  +  helium-4

16 8

O

+

1 1

H

13 7

N

+

4 2

He

(iv) oxygen-15   ¹⁵O, is made by bombarding nitrogen with positive deuterons (hydrogen-2)

nitrogen-14  +  hydrogen-2  ===>  oxygen-15  +  neutron

14 7

N

+

2 1

H

15 8

O

+

1 0

n

 A cyclotron can be used to produce positron emitting radioisotopes (beta plus emitters) used for PET scanning in medicine.

Other uses of particle accelerators

Particle accelerators are important complex pieces of apparatus that physicists use to investigate the most fundamental structure of nature from atomic nuclei to the various gigantic structures in the universe and how they function e.g. stars, black holes, how the 'Big Bang' began etc. etc.

By getting particles to smash into each other at speeds approaching that of light, all sorts of phenomena can be detected from the most fundamental particles that make up neutrons and protons, to super-heavy elements with life-times a tiny fraction of second.

Its very expensive technology - the Hadron Collider in Europe near Geneva, has cost billions of bounds to build and run. Its the most powerful particle accelerator ever built. It is supported by many countries and enables many scientists to collaborate with each other and share results and theoretical ideas.

7o. Summary  of key points about nuclear equations

A structured set of brief revision notes on nuclear equations tailored to GCSE/IGCSE and A level physics & chemistry syllabuses across AQA, Edexcel, OCR (Gateway & 21st Century), WJEC, CCEA, and Cambridge International.

Key Concepts

• Nuclear equation: Represents radioactive decay or nuclear reactions, showing conservation of proton number (atomic number) and nucleon number (mass number).
• General form:
  Lots of examples in e.g. sections 7d-7f.
• Conservation rules:
  • Mass number (A): total nucleons conserved.
  • Atomic number (Z): total protons conserved.
  • Charge and energy also conserved.

Types of Nuclear Decay

•  Alpha decay
  • Emits a helium nucleus (^4_2He).
  • Mass number decreases by 4, atomic number decreases by 2.
  • Example:

  • 7e. Alpha decay equations - nuclear expulsion of a helium nucleus

•    Beta-minus decay
  • Neutron → proton + electron + antineutrino.
  • Atomic number increases by 1, mass number unchanged.
  • Example:

  • 7f. Beta minus decay equations - nuclear expulsion of a negative electron

•     Beta-plus decay
  • Proton → neutron + positron + neutrino.
  • Atomic number decreases by 1, mass number unchanged.
  • Example:

  • 7h. Beta plus (positron) decay equations - nuclear expulsion of a positive electron (positron)

•      Gamma emission
  • Nucleus loses energy, no change in A or Z.
  • Example:

  • 7g. Gamma decay equations - nuclear expulsion of high energy gamma photon

Advanced Extensions

• Nuclear fission: splitting heavy nuclei (e.g. ²³⁵U into smaller nuclei + neutrons.
• Nuclear fusion: combining light nuclei (e.g. hydrogen isotopes) to form helium.
• Balancing equations: must conserve nucleon number, proton number, and energy.

Exam Tips

• Always check conservation of both A and Z.
• Write particles with correct notation:
• Show working clearly when balancing.

Common Misconceptions about nuclear equations

• Mixing up alpha and beta changes (students often wrongly add instead of subtracting).
• Thinking gamma changes A or Z (it does not).
• Confusing electron capture with beta-plus decay.
• Writing particles incorrectly (e.g. forgetting superscripts/subscripts).

Typical Syllabus Content

• GCSE/IGCSE (AQA, Edexcel, OCR Gateway/21st Century, WJEC, CCEA, CIE):
  • Alpha, beta, gamma decay equations.
  • Conservation of mass and atomic number.
  • Simple balancing tasks.
• A Level (AQA, Edexcel, OCR, WJEC, CCEA, CIE):
  • Full nuclear equations including neutrinos.
  • Fission and fusion equations.
  • Energy considerations (binding energy, mass defect).
  • Applications: nuclear power, astrophysics (fusion in stars).

Revision strategy:

• Practise balancing equations until automatic.
• Memorise particle symbols.
• Use exam board past papers to see isotope examples.
• Annotate equations with arrows showing changes in A and Z.

Atomic structure, history, definitions, examples and explanations including isotopes

1. Atomic structure and fundamental particle knowledge needed to understand radioactivity

2. What is Radioactivity? Why does it happen? Three types of atomic-nuclear-ionising radiation

3. Detection of radioactivity, its measurement and radiation dose units, ionising radiation sources - radioactive materials, background radiation

4. Alpha, beta & gamma radiation - properties of 3 types of radioactive nuclear emission & symbols ,dangers of radioactive emissions - health and safety issues and ionising radiation

5. Uses of radioactive isotopes emitting alpha, beta (+/–) or gamma radiation in industry and medicine

6. The half-life of a radioisotope - how long does material remain radioactive? implications!, uses of decay data and half-life values - archaeological radiocarbon dating, dating ancient rocks

7. What actually happens to the nucleus in alpha and beta radioactive decay and why? nuclear equations!, the production of radioisotopes - artificial sources of radioactive-isotopes, cyclotron

8. Nuclear fusion reactions and the formation of 'heavy elements' by bombardment techniques

9. Nuclear Fission Reactions, nuclear power as an energy resource

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Easier Foundation Tier Radioactivity multiple choice QUIZ

Harder Higher Tier Radioactivity multiple choice QUIZ

Worksheet QUIZ Question 1 on RADIOACTIVITY - absorption of alpha, beta and gamma radiation

Worksheet QUIZ Question 2 on RADIOACTIVITY - dangers & monitoring ionising radiation levels

Worksheet QUIZ Question 3 on RADIOACTIVITY - revision of atomic structure

Worksheet QUIZ Question 4 on RADIOACTIVITY - what happens to atoms in radioactive decay?

Worksheet QUIZ Question 5 on RADIOACTIVITY - uses of radioisotope and half-life data

ANSWERS to the WORD-FILL WORKSHEET QUIZZES

Crossword puzzle on radioactivity and ANSWERS!