Exam Study Notes

Physics of the Atom

Models of the Atom

• The understanding of atoms has evolved over time with new models replacing older ones as new experimental evidence emerges.
• A model describes something to explain its behavior.

Early Models

• Greek philosophers, like Democritus, proposed that matter consists of indivisible particles called 'atomos' (indivisible).
• Early models depicted atoms as small, solid, indivisible spheres.

Thomson's Plum Pudding Model

• J.J. Thomson discovered electrons at the end of the 19th century.
• Thomson proposed the plum pudding model: negatively charged electrons ('plums') embedded in a positively charged 'dough' or 'pudding'.
• Atoms were thought to be neutral, with positive charge balancing the negative electrons.

Geiger-Marsden Experiment (Rutherford's Gold Foil Experiment)

• Rutherford proposed a new model based on Geiger and Marsden's experiments.
• Alpha ($\alpha$) particles (positively charged) were directed at a thin gold foil in a vacuum.
• A fluorescent screen detected $\alpha$ particles by emitting faint flashes of light when hit.

Observations:

1. Most $\alpha$ particles passed straight through the foil.
2. A few $\alpha$ particles were deflected.
3. A very small number of $\alpha$ particles were reflected.

Conclusions:

1. Most of the atom is empty space (due to most particles passing through).
2. The deflection and reflection of $\alpha$ particles indicate repulsion by a concentrated positive charge.
3. The positive charge is concentrated in a very small volume.

Rutherford's Nuclear Model

1. The atom has a dense, central core called the nucleus, which is small compared to the atom's size.
2. The nucleus is positively charged.
3. Most of the atom's volume is empty space.
4. Negative electrons orbit the nucleus.
5. Rutherford also suggested the existence of a neutral particle (neutron) in the nucleus, supported by Chadwick's experiments in 1932.

The Nuclear Model

• Nearly all the mass of the atom is concentrated in the nucleus.
• The nucleus is positively charged.
• Negatively charged electrons orbit the nucleus at a distance.
• Rutherford's nuclear model replaced the plum pudding model because it better explained experimental observations.

Bohr Model

• Niels Bohr improved the atomic model in 1913, using the nuclear model as a base.
• Electrons orbit the nucleus at specific distances called energy levels.
• Up to 2 electrons can occupy the first energy level.
• Up to 8 electrons can occupy the second and third energy levels.

Successes of the Bohr Model

• The Bohr model explained experimental findings better than the nuclear model.
• It explained the absorption and emission of electromagnetic radiation.
• Theoretical calculations agreed with experimental results.

Discovery of the Neutron

• James Chadwick discovered the neutron in 1932.
• Chadwick bombarded beryllium with $\alpha$ particles, producing penetrating rays unaffected by magnetic or electric fields (indicating no charge).
• These rays ejected protons from paraffin, suggesting the neutral particles had approximately the same mass as a proton.

Timeline of Atomic Models

• Before 1897: Atoms were considered indivisible particles.
• 1897: J.J. Thomson discovered electrons as common constituents of all atoms.
• 1902-1907: Lord Kelvin and J.J. Thomson proposed the plum pudding model.
• 1906: Ernest Rutherford proposed the planetary model with electrons orbiting the nucleus.
• 1911: Geiger and Marsden's gold foil experiment supported Rutherford's nuclear model.
• 1913: Niels Bohr introduced stable electron orbits around the nucleus.
• 1932: J. Chadwick identified the neutron in the nucleus.
• Modern Day: Atoms contain a dense nucleus surrounded by a cloud of negative electrons. Electron position cannot be precisely pinpointed, exhibiting both wave and particle behavior.

Structure of the Atom

• Atom: The smallest component of an element that retains the element's properties.

Atomic Structure

• Atoms consist of a dense nucleus and a surrounding electron cloud.
• Electrons are negatively charged.
• The nucleus contains protons (positive charge) and neutrons (no charge).
• The number of protons equals the number of electrons, making the atom electrically neutral.

Relative Mass and Charge

Atomic Symbol / Nuclear Notation

• Notation: \frac{A}{Z}X where X is the atomic symbol, A is the mass number, and Z is the atomic number.
• Number of protons = Z.
• Number of neutrons = A - Z.
• Number of electrons = Number of protons = Z.

Atomic Number & Mass Number

• Atomic Number (Z): Number of protons in an atom.
• Mass Number (A): Number of protons + Number of neutrons.

Subatomic Particle Notation

Isotopes

• Isotopes: Atoms of the same element with the same number of protons but different numbers of neutrons.
• Isotopes have similar chemical properties but different masses.
• Some isotopes are radioactive.

Hydrogen Isotopes

• Hydrogen has three isotopes: \frac{1}{1}H (protium), \frac{2}{1}H (deuterium), and \frac{3}{1}H (tritium).
• Deuterium and tritium are found in seawater and the Sun.

Chlorine Isotopes

• Chlorine exists as two main isotopes: \frac{35}{17}Cl (75%) and \frac{37}{17}Cl (25%).
• Average atomic mass of chlorine: (0.75 \times 35) + (0.25 \times 37) = 35.5
• The atomic mass of chlorine in the Periodic Table is 35.5.

Example Problems

1. What are isotopes? Give an example of an element with isotopes.
2. Complete the table below:

• Which two atoms are isotopes?
• Which atom has the greatest mass?

More Example Problems

An atom has 14 protons and 20 neutrons.

• Its atomic number is:
  1. 14
  2. 16
  3. 34
• Its mass number is:
  1. 14
  2. 16
  3. 34
• The element is:
  1. Si
  2. Ca
  3. Se
• Another isotope of this element is:
  1. \frac{34}{16}X
  2. \frac{34}{14}X
  3. \frac{36}{14}X

Radioactivity

Discovery of Radioactivity

• In 1896, Henri Becquerel discovered radioactivity when uranium samples exposed and fogged covered photographic film.
• Marie Curie and her husband investigated uranium compounds and found:
  • Radiation emitted depends on the amount of the compound, not external conditions.
  • Polonium is 300 times more radioactive than uranium, and radium is 900 times more radioactive than uranium.
• Radioactive decay can be described as:
  • Parent nucleus \rightarrow daughter nucleus + particle

Types of Radiation

• Some atomic nuclei are unstable due to imbalanced forces.
• Carbon-14 (2 extra neutrons than carbon-12) is an unstable isotope of carbon.
• Unstable nuclei emit radiation (nuclear radiation) to become more stable.
• Radiation can be in the form of high energy particles or waves:
  • Alpha ($\alpha$)
  • Beta ($\beta^−$)
  • Gamma ($\gamma$)

Nature of Radiation

Alpha Particles(\alpha)

• Alpha particle: helium nucleus (2 neutrons and 2 protons).
• Charge: +2 (affected by electric fields).

Beta Particles ($\beta^−$)

• Beta particles: fast-moving electrons emitted from the nucleus.
• Charge: -1 (affected by electric fields).
• Produced when a neutron changes into a proton and an electron.

Gamma Rays ($\gamma$)

• Gamma rays: electromagnetic waves with the highest energy.
• No charge.

Properties of Nuclear Radiation

• Trend down the table:
  • The range & Penetrating power increases
  • Ionisation decreases

Cloud Chamber

• Used to detect radioactive emissions.
• Alpha particles: short, bold, wide, straight tracks (strongly ionizing).
• Beta particles: longer, fainter, thin, not necessarily straight tracks.
• Gamma rays: no tracks; if intense beam \rightarrow discontinuous, thin, irregular tracks.

Electric Field Effects

• Alpha particles (positive) are deflected away from the positive plate.
• Beta particles (negative) are deflected away from the negative plate.
• Gamma rays (no charge) are not deflected.
• Beta particles are deflected more than alpha particles due to their lighter mass.

Nuclear Transformations

• During radioactive decay, the atomic (proton) number and mass (nucleon) number will change.

Alpha Emission

• Alpha particle: 2 protons and 2 neutrons (helium nucleus).
• Emitted from large unstable nuclei.
• Nuclear notation for an alpha particle: \frac{4}{2}\alpha
  • The nucleus loses 2 protons \rightarrow atomic number decreases by 2.
  • The nucleus loses 4 particles \rightarrow mass number decreases by 4.

Beta Emission

• Beta decay: a neutron turns into a proton, emitting an electron.
• When a beta particle is emitted:
  • Number of protons increases by 1 \rightarrow atomic number increases by 1.
  • The mass number does not change.

Gamma Emission

• Gamma waves are emitted when the nucleus loses excess energy following decay.
• No protons or neutrons are lost.
• Atomic and mass numbers do not change.

Nuclear Equations

• Nuclear equations balance:
  • Sum of nucleon (mass) numbers on the left = sum on the right
  • Sum of proton (atomic) numbers on the left = sum on the right
• Parent nucleus: the nucleus that decays.
• Daughter nucleus: remaining nucleus after the decay.

Alpha Decay Equation

• The nucleon number of the daughter nucleus is 4 less than the parent.
• The proton number of the daughter nucleus is 2 less than the parent.

Beta Decay Equation

• The nucleon number of the daughter nucleus is the same as the parent.
• The proton number of the daughter nucleus is 1 more than the parent.

Gamma Decay Equation

• The nucleon number of the daughter nucleus is the same as the parent.
• The proton number of the daughter nucleus is the same as the parent.

The Random Nature of Decay

• Radioactive decay is a random process:
  • Equal probability of any nucleus decaying
  • Cannot know which nucleus will decay next or when.
  • Rate of decay is unaffected by surrounding conditions
  • It is only possible to estimate the probability of a certain nucleus decaying in a given time period
• It cannot be predicted when a particular unstable nucleus will decay

Half - Life

• Half-life is defined as:
  • The time taken for half the undecayed nuclei to decay or the activity of a source to decay by half.
• Different isotopes have different half-lives and half-lives can vary from a fraction of a second to billions of years in length

Half Life time

• The time it takes for the activity of the sample to decrease from 100 % to 50 % is the half-life
• It is the same length of time as it would take to decrease from 50 % activity to 25 % activity
• The half-life is constant for a particular isotope