1. Rutherford scattering:

• Figure 1 shows a plan view of the sort of apparatus that Geiger and Marsden used in 1911 to investigate the scattering of alpha particles by a thin foil of gold.
• Figure 1 A plan view of Geiger and Marsden’s apparatus.
• Gold was chosen because it can be hammered into very thin sheets.
• An alpha source was placed in a long thin lead container to produce a well-directed beam of alpha particles.
• The whole apparatus was evacuated so that the alpha particles could travel without being stopped by the air.
• Over a period of months, Geiger and Marsden counted the number of alpha particles deflected at different angles θ, shown in Figure 2.
• Figure 2 Only alpha particles that have a very close encounter with a gold nucleus are deflected through large angle
• The alpha particles were detected by a fluorescent screen.
• Each time an alpha particle hit the screen, a small flash of light was emitted, which was seen through the microscope.
• Geiger and Marsden counted hundreds of thousands of such flashes of light.
• The vast majority of the alpha particles were deflected through very small angles. But a very small number of particles were deflected through large angles of about 150° or more.
• Figure 2 illustrates some typical paths of deflected alpha particles.
• From this experiment, Rutherford came to the following findings.
  – The nucleus of the atom is minuscule and positively charged. Rutherford proposed that the positively charged alpha particle experiences a repulsive force that causes it to shift direction, and that this force is caused by the positive charge on the nucleus. The fact that only few particles experience a significant deflection indicates that the diameter of the nucleus is far lower than that of the atom.
  – The fact that almost all of an atom’s mass is contained in the nucleus is the second significant finding concerning it. The alpha particle would push aside a little nucleus, but it would rebound when coming into contact with a nucleus that is heavier than it. This is because of the conservation of momentum.
• By applying our understanding of electrostatic theory, we can determine the gold nucleus’s maximum size.
• If an alpha particle is flipped 180°, it must have collided with a gold nucleus directly and had to pause in motion for a brief period of time.
• The kinetic energy of the alpha particle has then been completely converted to electrical potential energy.

2. The structure of the nucleus has changed over time:

• Our understanding of the nucleus has undergone significant changes over time, reflecting advances in technology, experiments, and theoretical frameworks. Here’s a brief overview:
  1. Early days: Initially, atoms were thought to be indivisible. Discovery of radioactivity led to the understanding that atoms have a central nucleus.
  2. Rutherford’s model (1911): Ernest Rutherford proposed the planetary model, where electrons orbit a central nucleus.
  3. Nuclear force: In the 1930s, the strong nuclear force was discovered, which holds protons and neutrons together.
  4. Shell model: The 1940s saw the development of the nuclear shell model, explaining nucleon arrangement.
  5. Liquid drop model: The 1950s introduced the liquid drop model, describing nuclear behavior.
  6. Quark model: The 1960s revealed quarks as the building blocks of protons and neutrons.
  7. Standard Model: The 1970s established the Standard Model of particle physics, incorporating quarks and forces.
  8. Modern understanding: Today, we know the nucleus comprises protons and neutrons (made up of quarks), held together by the strong nuclear force, with a complex structure and interactions.
• Our understanding of the nucleus has evolved significantly over time, reflecting advances in science and technology. From simple models to the modern Standard Model, our knowledge continues to refine and expand.

α, β,and γ radiations

3. The nature of alpha (α), beta (β), and gamma (γ) radiations:

• Unstable nuclei emit various types of radiation, the most common of which are alpha, beta and gamma radiation. Their nature and properties are

• ⇒ Alpha (α) particles:

• Alpha particles are the nuclei of helium atoms.
• So, they are made up of two protons and two neutrons. They have a mass of 4u and a charge of .
• Alpha particles are strongly ionising.
• The strong charge on the alpha particle pulls electrons out of atoms, creating pairs of positive and negative ions along the particle’s path (Figure 3).
• Figure 3 The strong electric field of the alpha particles pulls or knocks electrons out of atoms to create positive and negative ions.
• An alpha particle produces about 10000 ion-pairs per millimetre of path in air.
• Alpha particles travel a few centimetres in air, and can be stopped by a thick piece of paper (Figure 4).
• Alpha particles are deflected slightly in strong electric and magnetic fields. Typically, alpha particles have kinetic energies of a few MeV as they leave the parent nucleus.
• An alpha particle with an energy of 5MeV travels at about 5% of the speed of light.

• ⇒ Beta (β) particles:

• Beta particles are fast-moving electrons, which travel at just less than the speed of light.
• Typically, beta particles have kinetic energies of a few MeV.
• Beta particles are much less ionising than alpha particles, producing about 100 ion-pairs per millimetre of path travelled in air.
• Beta particles may travel several metres in air, and they are absorbed by aluminium a few millimetres thick (Figure 4).
• Beta particles may be deflected through large angles by electric and magnetic fields.
• Figure 4 The penetrating powers of alpha, beta and gamma radiations.

• ⇒Gamma (γ) particle:

• Gamma rays are electrically neutral emissions, which are photons (just like any other type of electromagnetic radiation).
• Typically, a gamma-ray photon might have an energy of about 1 MeV, which corresponds to a wavelength of about [math] 10^{-12} m[/math].
• Gamma rays are not deflected an magnetic and electric fields because they are not charged.
• Gamma rays are very weakly ionising, producing about one ion-pair per millimetre of path travelled in air.
• Gamma rays are very penetrating, and their intensity is reduced by a few centimetres thickness of lead (Figure 4).
• Gamma rays can transfer their energy to electrons in metals (rather like a photoelectric effect); then the moving electrons create ion-pairs.
• Experimental identification:
  – Absorption experiments: Measure the absorption of radiation by different materials
  – Spectroscopy: Analyze the energy distribution of radiation
• Applications:
  Relative hazards of exposure to humans:
  – Alpha particles: Most harmful, but easily stopped
  – Beta particles: Moderately harmful, requires some shielding
  – Gamma rays: Most penetrating, requires thick shielding
  Radiation protection and safety measures:
  – Medical applications: Radiation therapy, diagnostic imaging
  – Industrial applications: Radiation sterilization, food irradiation
• By understanding the properties and experimental identification of ionizing radiation, we can assess the relative hazards of exposure to humans and develop appropriate safety measures and applications.

4. Inverse square law of γ radiation:

• Gamma radiation behaves like any other electromagnetic radiation, in that it spreads out symmetrically in all directions from its source.
• The intensity of a light source obeys an inverse square law.
• For gamma radiation we can write
• [math] I = \frac{k}{x^2} [/math]

• Where I is the intensity of the radiation (which can be measured in [math] W.m^{-2} [/math]), x is the distance from the source and k is constant.

5. Experimental verification of inverse-square law:

• (Note: This is just one example of how you might tackle this required practical).
• Figure 5 shows an experimental arrangement to investigate the relationship between the intensity of radiation from a gamma source and its distance from a Geiger-Muller tube.
• Figure 5
• In Figure 5, x has been defined as the distance between the edge of the source container and the window of the GM tube.
• However, there is a difficulty with this definition. The source itself is inside the container, and the radiation is not all detected at the window of the tube.
• So, the true distance between the source and the place where the radiation is detected is x + c. This is called the corrected distance.
• So, we write
• [math]  I = \frac{k}{[x + c]^2} \\
  [x + c]^2 = \frac{k}{I} \\
  x + c = \left(\frac{k}{I}\right)^{\frac{1}{2}} [/math]
• Therefore, if we plot a graph of x against [math]I^{-1⁄2} [/math], we would expect to see a straight line.
  In an experiment, the results shown in table 1 were obtained.
  The background count was determined to be an average of 18 counts per minute.
• Table 1
• 1) Copy the table and add two further rows to it.
• 2 a) Make a suitable correction allowing for background count and add to your table.
• b) Add a further row to show [math] \text{[count rate]}^{-\frac{1}{2}} [/math]
  3 a) Plot a suitable graph to investigate whether the intensity of the gamma radiation obeys an inverse square law. 
  b) Use your graph to estimate the value of c shown in Figure 5.

6. Safe handling of radioactive sources:

• Safe handling of radioactive sources is crucial to minimize exposure and prevent accidents. Here are some guidelines:
  1. Training: Ensure that all personnel handling radioactive sources are properly trained and authorized.
  2. Personal Protective Equipment (PPE): Wear appropriate PPE, such as gloves, masks, and suits, to prevent skin contact and inhalation.
  3. Storage: Store radioactive sources in designated areas with proper shielding and security.
  4. Labeling: Clearly label all radioactive sources and containers with warning signs and radiation symbols.
  5. Handling: Use tongs, forceps, or other tools to handle radioactive sources, avoiding direct contact.
  6. Shielding: Use lead or concrete shielding to minimize radiation exposure.
  7. Monitoring: Regularly check radiation levels and monitor for contamination.
  8. Transportation: Ensure safe transportation of radioactive sources, using appropriate containers and vehicles.
  9. Disposal: Follow proper procedures for disposing of radioactive waste and sources.
  10. Emergency Response: Have a plan in place for accidents or spills, including notification, containment, and decontamination procedures.
  11. Regulatory Compliance: Adhere to relevant laws, regulations, and guidelines for handling radioactive sources.
  12. Continuous Training: Regularly update training and procedures to reflect changes in regulations, technology, and best practices.
• By following these guidelines, you can ensure the safe handling of radioactive sources and minimize the risk of exposure and accidents.

7. Background radiation:

• There are a lot of rocks in the Earth that contain radioactive uranium, thorium, radon and potassium, and so we are always exposed to some ionising particles. Radon is a gas that emits alpha particles.
• Because we can inhale this gas, it is dangerous as radiation can get inside our lungs.
• In addition, the Sun emits lots of protons, which can also create ions in our atmosphere.
• These are two of the sources that make up background radiation.
• Figure 6 shows the contribution to the total background radiation from all places in Britain.
• Figure 6 Sources of radiation in Britain.
• Fortunately, the level of background radiation is quite low, and in most places, it does not cause a serious health risk.
• In some jobs workers are at a higher risk.
• X-rays used in hospitals also cause ionisation.
• Radiographers make sure that their exposure to X-rays is as small as possible.
• In nuclear power stations, neutrons are produced in nuclear reactors.
• The damage caused by neutrons is a source of danger for workers in that industry.

8. Risk and benefits in the uses of radiation in medicine:

• The use of radiation in medicine involves a delicate balance between risk and benefits. Radiation can be used to:
• Benefits:
  1. Diagnose: Radiation helps diagnose diseases, such as cancer, through imaging technologies like X-rays, CT scans, and PET scans.
  2. Treat: Radiation therapy treats cancer, reducing tumor size and relieving symptoms.
  3. Research: Radiation helps develop new treatments and medications.
• Risks:
  1. Cancer risk: Ionizing radiation increases cancer risk, especially in high doses or prolonged exposure.
  2. Genetic damage: Radiation can cause genetic mutations, potentially leading to health issues.
  3. Tissue damage: High doses can cause tissue damage, burns, or organ dysfunction.
• To strike a balance:
  1. Optimize doses: Use the lowest effective dose for diagnosis and treatment.
  2. Alternative methods: Consider alternative imaging modalities, like MRI or ultrasound, when possible.
  3. Shielding: Use shielding to minimize exposure.
  4. Monitoring: Closely monitor patients and staff for radiation exposure.
  5. Education: Inform patients and staff about radiation risks and benefits.
  6. Research: Continuously research ways to minimize risks and maximize benefits.
  7. Regulation: Adhere to established guidelines and regulations.
• By acknowledging and addressing the risks, we can harness the benefits of radiation in medicine while ensuring patient and staff safety.