Topic 5 · Nuclear physics

How many neutrons are there in a nucleus of ²³⁵₉₂U?

1. A92
2. B143
3. C235
4. D327

A radioactive source is placed near a detector. A sheet of paper does not reduce the count rate, but a 5 mm sheet of aluminium reduces it almost to background. What does the source emit?

1. Aα-particles only
2. Bβ-particles only
3. Cγ-rays only
4. Dα-particles and γ-rays

A sample of a radioactive isotope has an activity of 800 Bq. The half-life of the isotope is 6.0 hours. What is the activity after 24 hours?

1. A0 Bq
2. B50 Bq
3. C200 Bq
4. D400 Bq

A nucleus of ²²⁶₈₈Ra decays by emitting an α-particle. What is the nuclide produced?

1. A²²²₈₆Rn
2. B²²²₈₈Ra
3. C²²⁶₈₆Rn
4. D²²⁶₈₉Ac

Which is not a source of background radiation?

1. Acosmic rays reaching the Earth from space
2. Bradon gas seeping from rocks and soil
3. Cthe Earth's magnetic field
4. Dnaturally occurring isotopes in food and drink

A smoke alarm contains a source that ionises the air in a small gap, allowing a tiny current to flow. Smoke entering the gap reduces the current and sets off the alarm. Which source is most suitable?

1. Aan α-emitter with a half-life of several hundred years
2. Ban α-emitter with a half-life of a few hours
3. Ca γ-emitter with a half-life of several hundred years
4. Da β-emitter with a half-life of a few days

In the α-particle scattering experiment, a beam of α-particles was directed at a very thin sheet of gold foil in an evacuated container. Most α-particles passed straight through with little or no deviation. A small number were deflected through large angles, and about one in 8000 was deflected through more than 90°.

1. (a)

   Explain Explain what the observation that most α-particles passed straight through tells us about the structure of the atom.

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   1. 1

      most of the atom is empty space

   2. 2

      so most α-particles pass through the foil without coming close to anything that can deflect them

2. (b)

   Explain Explain what the small number of α-particles deflected through more than 90° tells us about the nucleus.

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   1. 1

      the positive charge and almost all the mass of the atom are concentrated in a very small volume — the nucleus

   2. 2

      the α-particle is positive, so it is repelled strongly when it passes very close to a nucleus

   3. 3

      such a close approach is rare, which is why so few particles are deflected through large angles

3. (c)

   Suggest Suggest why the container had to be evacuated and the gold foil had to be very thin.

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   1. 1

      α-particles are absorbed by only a few centimetres of air, so air in the container would stop them before they reached the foil or the detector

   2. 2

      a thin foil ensures each α-particle is scattered by at most one nucleus, so the deflections can be interpreted

Carbon has two naturally occurring stable isotopes, ¹²₆C and ¹³₆C, and one radioactive isotope, ¹⁴₆C, which decays by β-emission to nitrogen.

1. (a)

   Define Define the term isotope.

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   1. 1

      atoms of the same element, with the same number of protons (same proton number)

   2. 2

      but different numbers of neutrons (different nucleon number)

2. (b)

   Explain Explain why the three isotopes of carbon all behave identically in chemical reactions.

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   1. 1

      chemical behaviour is determined by the electrons, particularly the outer electrons

   2. 2

      all three isotopes have 6 protons and therefore the same number and arrangement of electrons

3. (c)

   State Complete the decay equation for carbon-14, giving the nucleon and proton numbers of the nitrogen nucleus produced: ¹⁴₆C → ᴬ_Z N + ⁰₋₁β

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   1. 1

      Conservation of nucleon number gives A = 14 for the nitrogen nucleus.

   2. 2

      Conservation of proton number gives Z = 7 for the nitrogen nucleus.

4. (d)

   Explain A β-particle is an electron, yet there are no electrons in a nucleus. Explain where the emitted β-particle comes from.

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   1. 1

      a neutron in the nucleus changes into a proton

   2. 2

      and an electron is created and emitted at that moment, which is why the proton number rises by one while the nucleon number is unchanged

A hospital uses a radioactive tracer to study a patient's kidneys. The tracer is a γ-emitter with a half-life of 6 hours and is injected into the bloodstream.

1. (a)

   Define Define half-life.

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   1. 1

      the time taken for half the nuclei of the radioactive isotope in a sample to decay

   2. 2

      or, equivalently, for the activity (count rate) of the sample to fall to half its original value

2. (b)

   Explain Explain why a γ-emitter is chosen for this use rather than an α-emitter.

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   1. 1

      γ-rays are the most penetrating of the three, so they pass out through the body and can be detected outside it

   2. 2

      α-particles would be absorbed within a few centimetres of tissue and never reach the detector

   3. 3

      α is the most strongly ionising, so it would do far more damage to the surrounding cells

3. (c)

   Suggest Suggest why an isotope with a half-life of 6 hours is more suitable than one with a half-life of 6 years.

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   1. 1

      the activity falls quickly once the measurement is finished, so the patient's total exposure is small

   2. 2

      an isotope with a half-life of years would keep irradiating the patient long after the scan, with no benefit

A student determines the half-life of a radioactive source using a Geiger–Müller tube and a counter. Before bringing out the source, she records the count over 10 minutes with no source present and obtains 240 counts. She then places the source at a fixed distance from the tube and records the count rate every 20 minutes.

1. (a)

   Determine Determine the background count rate, and explain why it must be measured.

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   1. 1

      background count rate = 240 / 10 = 24 counts per minute

   2. 2

      radiation from cosmic rays, rocks, and other natural sources is detected as well as the source, so it must be subtracted from every reading to obtain the count rate due to the source alone

2. (b)

   Determine Correct the readings for background and hence determine the half-life of the source.

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   1. 1

      subtracts 24 from every reading: corrected rates 380, 190, 95, 48, 24 counts per minute

   2. 2

      identifies that the corrected rate halves from 380 to 190 between 0 and 20 minutes

   3. 3

      checks a second interval — 190 falls to 95 over the next 20 minutes, and 95 to 48 over the next

   4. 4

      half-life = 20 minutes

3. (c)

   Suggest The student's corrected values do not halve over exactly equal intervals. Suggest why, and suggest one improvement to the experiment.

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   1. 1

      radioactive decay is a random process, so the count in any fixed interval fluctuates

   2. 2

      improvement: count over a longer interval at each time, take repeat readings, or plot all the corrected values on a graph and take the half-life from a smooth curve