Structure of the Atom Study Notes: Structure of Atom and Radioactivity

Properties of Cathode and Anode Rays

• Cathode Rays

  • They originate from the cathode.

  • They travel in straight lines.

  • The particles constituting them have a negative charge ($\theta$ represents negative sign in notes, verified as electrons).

  • Their properties and the particles themselves do not depend on the nature of the gas filled in the discharge tube.

  • They have the ability to ionize gases they pass through.

  • They possess kinetic energy.

  • The charge and mass of these particles do not depend on the material of the cathode.

• Anode Rays (Canal Rays)

  • They originate from the side of the anode (produced by the ionization of molecules of the residual gas).

  • They travel in straight lines.

  • The particles forming them have a positive charge.

  • Their properties and the $\frac{e}{m}$ (charge-to-mass ratio) value depend on the nature of the gas filled in the tube.

  • Being positively charged particles, they are deflected by electrical and magnetic fields.

Fundamental Particle Data and Constants

• Electron ($e$)

  • Charge ($e$): $-1.6 \times 10^{-19}\,C$

  • Charge-to-mass ratio ($\frac{e}{m}$): $1.76 \times 10^{11}\,C/kg$

  • Mass computation: One electron mass is calculated as the charge divided by the $\frac{e}{m}$ ratio.

Thomson Model of the Atom

• Successful Explanations

  • The Thomson model could correctly explain the overall neutrality of the atom.

• Failure to Explain

  • It failed to explain the spectra of the hydrogen atom.

  • It could not accurately determine the positions of electrons, protons, and neutrons within the atom.

  • It failed to explain the stability of the atom.

Radioactivity

• Discovery

  • 
    

    Henri Becquerel discovered that some elements emit radiation naturally, a phenomenon known as radioactivity. Elements that exhibit this behavior are called radioactive elements.

• Types of Radiations

  • Alpha ($\alpha$) rays: These consist of high-energy particles with two positive charges and a mass of four atomic units. They are identical to helium nuclei ($He^{2+}$).

  • Beta ($\beta$) rays: These are negatively charged particles, identical to electrons ($\beta = e^{-}$).

  • Gamma ($\gamma$) rays: These consist of high-energy, neutral radiation similar to X-rays. They do not consist of particles and have no charge.

• Penetrating Power

  • The order of penetrating power for these radiations is: $\gamma > \beta > \alpha$.

Rutherford's Alpha Particle Scattering Experiment

• Experimental Setup

  • Rutherford and his students bombarded a thin gold foil (thickness approximately $100\,nm$) with high-energy alpha particles.

  • Alpha particles were emitted from a radioactive source.

  • A circular fluorescent zinc sulphide (ZnS) screen was placed around the gold foil.

  • Tiny flashes of light (scintillations) were produced on the screen whenever a particle struck it.

• Observations

  • Most of the alpha particles (nearly $99\%$) passed through the gold foil undeflected.

  • some of the alpha particles were deflected by small angles.

  • A very small fraction (approximately $1$ in $20,000$) bounced back (deflected by $180^{\circ}$).

• Conclusions

  • Since most particles pass through undeflected, most of the space inside an atom is empty.

  • Because some particles were deflected by small angles, it indicates the positive charge in an atom is concentrated in a very small region at the center, which Rutherford named the nucleus.

  • The fact that very few particles bounced back indicates that the size of the nucleus is extremely small compared to the size of the atom.

Rutherford's Nuclear Model of the Atom

• Core Principles

  • Most of the mass and all of the positive charge of an atom is concentrated in a very small region called the nucleus.

  • The size of the nucleus is extremely small compared to the size of the atom.

  • Dimensions:

    • Radius of the nucleus: approximately $10^{-15}\,m$.

    • Radius of the atom: approximately $10^{-10}\,m$.

  • The magnitude of the charge on the nucleus varies for atoms of different elements.

  • The nucleus is surrounded by electrons that revolve around it at very high speeds. This model is often referred to as the Planetary Model.

  • The total negative charge of the electrons is equal to the total positive charge on the nucleus, ensuring the atom is electrically neutral overall.

  • Electrons and the nucleus are held together by electrostatic forces of attraction.

• Drawbacks

  • It failed to explain the stability of atoms (accelerated charges should emit energy and collapse).

  • it could not explain the electronic structure of the atom (distribution and energy of electrons).

  • It failed to explain the existence of specific definite lines in the hydrogen spectrum.

Atomic Representation and Properties

• Moseley's Findings

  • Through X-ray experiments, Moseley discovered that the identity of an atom is defined by its atomic number ($Z$), not its atomic weight.

  • Atomic Number ($Z$) = number of protons ($p$).

  • Mass Number ($A$) = number of protons ($p$) + number of neutrons ($n$).

• IUPAC Element Representation

  • Elements are represented as $_{Z}^{A}X$, where:

    • $X$ is the symbol of the element.

    • Superscript $A$ is the Mass Number.

    • Subscript $Z$ is the Atomic Number.

  • Example: Sodium ($_{11}^{23}Na$) contains:

    • $Z = 11$ (Protons)

    • $e = 11$ (Electrons in a neutral atom)

    • $n = A - Z = 23 - 11 = 12$ (Neutrons)

Atomic Species Classifications

1. Isotones

Atoms of different elements having the same number of neutrons in the nucleus.

• Examples:

  • $_{6}^{14}C$: $n = 14 - 6 = 8$

  • $_{7}^{15}N$ : $n = 15 - 7 = 8$

  • $_{8}^{16}O$: $n = 16 - 8 = 8$

1. Isoelectronic Species

   • Atoms, molecules, or ions that have the same total number of electrons.

   • Examples (all with $10$ electrons):

     • $N^{3-}$ ($7 + 3 = 10$)

     • $O^{2-}$ ($8 + 2 = 10$)

     • $F^{-}$ ($9 + 1 = 10$)

     • $Ne$ ($10$)

     • $Na^{+}$ ($11 - 1 = 10$)

     • $Mg^{2+}$ ($12 - 2 = 10$)

     • $Al^{3+}$ ($13 - 3 = 10$)

2. Isodiaphers

   • Atoms having the same difference between neutrons and protons ($N - Z$).

   • Example 1: $_{19}^{39}K$

     • $p (Z) = 19, n (N) = 20$

     • $N - Z = 20 - 19 = 1$

   • Example 2: $_{9}^{19}F$

     • $p (Z) = 9, n (N) = 10$

     • $N - Z = 10 - 9 = 1$

   • Note: The parent and daughter nuclides in $\alpha-radioactive$ decay are isodiaphers.

Questions & Discussion

• Q: Total number of electrons in 1 mole of methane ($CH_{4}$)?

  • Analysis: 1 molecule of methane ($CH_{4}$) contains $6$ (from C) + $4$ (from 4H) = $10$ electrons.

  • Total in one mole = $10 \times 6.022 \times 10^{23}$.

• Q: Correct symbol for species with $e = 18, p = 16, n = 16$?

  • Analysis: Protons ($p = 16$) identify the element as Sulfur ($S$).

  • Mass number ($A$) = $p + n = 16 + 16 = 32$.

  • Charge = $p - e = 16 - 18 = -2$.

  • Symbol: $_{16}^{32}S^{2-}$.

• Q: What is wrong about anode rays?

  • Answer: "Their $\frac{e}{m}$ ratio is constant." Correct fact: $\frac{e}{m}$ varies with the nature of the gas.

• Q: Which statement is incorrect regarding cathode rays?

  • Answer: "Charge and mass of the particles constituting cathode rays depends upon the nature of the gas." Correct fact: They are independent of the gas nature.

• Q: How many neutrons are in $_{38}^{88}Sr$?

  • Calculation: $n = A - Z = 88 - 38 = 50$.