Why are some isotopes more stable than others? In what ways can a nucleus undergo change?

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How do large, unstable nuclei become more stable?

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How can the random nature of radioactive decay allow for predictions to be made?

Understandings (SL)

• isotopes
• nuclear binding energy and mass defect
• the variation of the binding energy per nucleon with nucleon number
• the mass-energy equivalence in nuclear reactions
• the existence of the strong nuclear force, a short-range, attractive force between nucleons
• the random and spontaneous nature of radioactive decay
• the changes in the state of the nucleus following alpha, beta and gamma radioactive decay
• the radioactive decay equations involving ,-,+,
• the existence of neutrinos and antineutrinos ‾
• the penetration and ionising ability of alpha particles, beta particles and gamma rays
• the activity, count rate and half-life in radioactive decay
• the changes in activity and count rate during radioactive decay using integer values of half-life
• the effect of background radiation on count rate.

Understandings (AHL)

• the evidence for the strong nuclear force
• the role of the ratio of neutrons to protons for the stability of nuclides
• the approximate constancy of binding energy curve above a nucleon number of 60
• that the spectrum of alpha and gamma radiations provides evidence for discrete nuclear energy levels
• the continuous spectrum of beta decay as evidence for the neutrino
• the decay constant and the radioactive decay law
• that the decay constant approximates the probability of decay in unit time only in the limit of sufficiently small λt
• the activity as the rate of decay
• the relationship between half-life and the decay constant

Guidance (SL):

• An interpretation of binding energy curves is required.
• Nuclear masses will be expressed in kg, in MeVc^-2 and in (unified) atomic mass units u.
• Real-life contexts for this topic should include the choice of isotope in medical use, leaks in underground pipes, thickness of materials, and radioactive dating based on the penetration of the decay particle and half-life.
• The weak nuclear force is not considered in this course.
• The determination of the half-life of a nuclide is required.

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Guidance (HL):

• An application of the radioactive decay equations for arbitrary time intervals is required for an additional higher level.

The average person receives about 2.4 millisieverts (mSv) of background radiation per year from natural sources like cosmic rays and terrestrial radiation.

Nuclear Regulatory Commission: For the public, the limit for radiation exposure is 100 mrem (1 mSv) per year above background levels.

Which is the most radioactive place on Earth?

Henri Becquerel & Marie Curie

Video: Discovery

Stop the video at the discovery moment:

Propose possible hypotheses about what the mysterious rays might be.

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Testing experiments for Becquerel rays

One of the explanations of Becquerel’s experiments is that uranyl salts emit some kind of charged particles that affect the photosensitive paper in a way similar to light. How can you test this explanation?

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Curie’s experiments (a bit of chemistry…)

Pierre Curie invented an electrometer that could be used to measure how much charge the electrometer loses per unit time (the current). Marie Curie used it to measure the amount of current produced when the electrometer was placed near uranium salts. She found that

• the amount of current was proportional to the amount of uranium present.
• the intensity of the current was independent of the chemical structure of the uranium salt (as long as it contained uranium), its wetness, temperature, physical appearance, or the amount of light shining on it.

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a. Explain why the electrometer could lose its charge when a sample of uranium salt was placed nearby.

b. If you were Marie Curie, with a strong background in chemistry, what could you conclude about how the uranium rays are produced? (Hint: Sometimes in science you can determine what a phenomenon is not long before you have an idea about what it is.)

Explain…

In 1899 Ernest Rutherford and his colleagues investigated the ability of uranium salts to ionize air. He set up two parallel plates, with a potential difference between them.

When a uranium sample was placed between the plates, ions created by the radiation would be pulled to the plates before they could recombine. This caused a detectable current. Covering the uranium sample with thin aluminum sheets decreased the amount of current observed, but only up to a point. After this point, no further decrease in current was observed, even with the addition of more aluminum plates.

Propose an explanation of why the current decreased with more aluminum shielding, but only to a point.

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Explain

In 1903 Rutherford placed his radioactive sample in a magnetic field in an apparatus such as that shown below. He and his assistants used a scintillating screen, which glowed when a charged particle hit the surface (similar to the screen of an old-fashioned TV that has a cathode-ray tube inside). In the second experiment they used photographic paper and found that it was exposed around point O (in this experiment the photographic paper was wrapped in a cover). Describe below the cause of each exposure.

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a. Describe everything you can about what caused the glowing screen at space 1.

b. Describe everything you can about what caused the glowing screen at space 2.

c. Describe everything you can about what caused the photographic paper to be exposed at O.

Evaluate the reasoning

Based on the experiments such as the one described above, scientists proposed the following model of an atomic nucleus (later found to be incorrect). The nucleus of an atom is made of positively charged alpha particles and negatively charged electrons. Their electrostatic attraction holds them together. When a nucleus has a lot of alpha particles, they start repelling each other and are likely to leave the nucleus (alpha decay). This leaves too many electrons inside that repel each other and thus electrons are emitted (beta decay). After each transformation the nucleus is left in an excited state and emits a high-energy photon—a gamma ray (gamma decay).

According to Heisenberg’s uncertainty principle, the uncertainties of the position and momentum of an atomic-size particle can be simultaneously known no better than determined by the following equation

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Experiments by Rutherford’s colleagues led to the estimation of the size of atomic nucleus to be about

You can then apply the uncertainty principle to find the momentum, and then the energy, of the electron inside the nucleus.

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Can the electron be inside the nucleus?

We can then calculate the potential energy of the electron inside the nucleus:

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Adding this to its E_k, the total energy works out to be positive.

Why doesn’t the nucleus burst apart?

RADIOACTIVE DECAY

Are all nuclei stable? What is nuclear stability?

https://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_en.html

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RADIOACTIVE DECAY:: emission of ionizing radiation (alpha, beta or gamma radiation) caused by the changes in the nuclei of unstable atoms.

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Decay of an unstable nucleus is always:

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1. Spontaneous
2. Random
3. Unpredictable
4. Uncontrollable

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How do nuclei decay?

Nuclear decay

Radioactive atoms decay because their nuclei are unstable (later)

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They emit alpha, beta or gamma radiation

2

4

He

β

-1

0

γ

2

4

𝛼

e

-1

0

Alpha decay

Alpha particles - properties

• Big particles → lots of collisions → they stop easily (piece of paper)
• Range in air 5-8 cm
• Strong ionising power

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Alpha radiation generic equation

ALPHA RADIATION

= emission of a He-4 nucleus

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Gamma decay

Gamma rays properties

• They are neutral →they do not interact much with material → weak ionisation power but strong penetrating power
• Their range in air is virtually infinite!
• We can shield ourselves from gamma radiation only with thick lead or boron paraffine.

Gamma radiation

GAMMA RADIATION

= emission of a high energy photon

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Gamma photons and Alpha particles have discrete energies (i.e. specific energies, not continuous energy spectrum - evidence of nuclear energy levels!).

Beta particles properties

• They are charged particles but much smaller than alpha particles → medium penetration power
• Medium ionisation power
• They can be stopped using thin aluminium
• Range in air 5-10m

Nuclear energy levels (HL)

Alpha decay - its kinetic energy equals to the energy difference between the nucleus’ initial and final state → the energy should be discrete.

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Beta radiation general equation

BETA MINUS DECAY:

neutron decays into a proton, electron and anti-neutrino

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BETA PLUS DECAY:

proton decays into a neutron, positron and neutrino

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We needed the neutrino to explain the range of kinetic energies.

Effects of radiation on cells at atomic level

Ionization

Excitation

Biological Effects�Mechanisms of Injury

Ionizing Radiation

Cell Damage

Repair

Transformation

Mechanisms of damage at molecular level

Bond breaks

Direct action:

Breaking strands of DNA

Indirect action:

Via free radicals

Ionising radiation

• Short term
• Skin burns
• Nausea
• GI bleeding
• Death
• Long term
• Cancer
• Death

Decay Chains

Thorium decays by the decay series shown below. What do the blue and red arrows represent?

Half life is the time taken for the number of radioactive nuclei to fall to half (learn definition!)

View Sim

TASK. 5.4.1 Investigating Half Life

Radioactive decay law (HL)

The law of radioactive decay states

the higher the number of radioactive nuclei, the higher the rate of decay.

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Show that an exponential decay satisfies this equation.

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The decay equation

Decay equation

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Solutions

Decay constant

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In your groups, derive the relationship between the half life and the decay constant.

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Decay constant and half life

Half life is the time taken for the number of radioactive nuclei to fall to half (learn definition!)

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Activity

The activity is the number of nuclei decaying per second. It is the same as the decay rate.

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It is measured in Bq, one Bq is one decay per second.

What is the relationship between A and N?

Draw a graph of A vs N.

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Exam practice

Nuclear reactions, fission and fusion

Atomic masses are often given in terms of atomic mass unit.

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One atomic mass unit is defined as one twelfth of the mass of a C-12 atom�

1 u = 1/12(19.92x10^-27)kg = 1.66x10^-27 kg

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The mass of electrons, protons and neutrons are given below. Find the mass of a Helium nucleus in atomic mass units

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Learn definition!

4.031882 u

Mass of He nucleus 4.001508 u

Mass  Defect

Where does the missing mass go?

E = mc²

Why does fusion in stars stop at iron?

How much energy corresponds to 1u?

Please give your answer in Joules and in eV.

Energy released in fusion

Calculate the energy released in these reactions

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Δm=5.3 x 10^-3 u

E=5 MeV

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Mass of proton 1.007276 u

Mass of deuterium 2.014102 u

Mass of tritium 3.016049 u

Mass of He-4 4.002602 u

Mass of He-3 3.016029 u

Mass of neutron 1.008665 u

40 million Kelvin temperature to overcome the “Coulomb barrier”.

Energy released in nuclear decays

What is the energy released in these decays?

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The minimum kinetic energy needed is

0.00128 x 931.5 = 0.68 MeV.

Grade Gorilla - Binding Energy

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Grade Gorilla - Radioactive Decay

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Paper Plainz

1. Try first

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• Then ask a buddy

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• Then look at the Answer (not the video solution) to see if you can work it out

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• Then look at the video solution

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• Then ask your teacher

Higher Level