Atomic Structure

2.1.1 Explain the construction and working of discharge tube with reference to the discovery of electron and proton;

• • Construction: The discharge tube, a sealed glass apparatus, consists of:
    • A cathode (negative electrode) and an anode (positive electrode) at opposite ends.
    • A side tube connected to a vacuum pump to control the gas pressure.
    • The tube is filled with a gas (e.g., air, hydrogen) at very low pressure.
    • A high-voltage power supply is connected to the electrodes.

• • Working (Electron Discovery – Cathode Rays):
    • When a high voltage (thousands of volts) is applied, the gas molecules become ionized.
    • At very low pressure, the mean free path of electrons increases, allowing them to accelerate without frequent collisions.
    • Cathode rays, streams of negatively charged particles, are emitted from the cathode.
    • These rays cause the glass tube to fluoresce, indicating their presence.

• • Working (Proton Discovery – Canal Rays):
    • Goldstein modified the discharge tube by using a perforated cathode.
    • When a high voltage was applied, positively charged rays were observed passing through the holes in the cathode, moving towards the negative electrode.
    • These “canal rays” or “positive rays” are ions formed when electrons collide with gas molecules, removing electrons.
    • In the case of hydrogen gas, the positive ions are protons.

2.1.2 Describe the properties of:

a. Cathode rays:

• • • Straight-line propagation: They travel in straight lines, casting shadows of objects placed in their path.
    • Negative charge: They are deflected by both electric and magnetic fields, indicating their negative charge. The direction of deflection confirms this.
    • Independence of gas: The nature of cathode rays is independent of the gas used in the discharge tube, suggesting they are fundamental particles of all atoms.
    • Constant e/m ratio: The charge-to-mass (e/m) ratio of cathode rays is constant, indicating they are identical particles (electrons).

b. Positive rays:

• • • Positive charge: They are deflected by electric and magnetic fields in the opposite direction to cathode rays.
    • Gas dependence: The e/m ratio of positive rays varies with the gas used in the discharge tube, because the positive ions formed depend on the gas.
    • Hydrogen’s special case: Hydrogen gas produces positive rays with the highest e/m ratio, indicating that the proton is the lightest positive particle.

2.2 Planck’s Quantum Theory: Energy in Discrete Packets

2.2.1 Explain the relationship among energy, frequency, wavelength and wave number using Planck’s quantum theory;

• • Quantization of Energy: Planck proposed that energy is not continuous but is emitted or absorbed in discrete packets called quanta.
  • Planck’s Equation (E = hν):
    • E represents the energy of a quantum.
    • h is Planck’s constant (6.626 x 10^-34 J·s).
    • ν (nu) is the frequency of the radiation.
  • Relationship to Wavelength (ν = c/λ):
    • Frequency (ν) is related to wavelength (λ) by the equation ν = c/λ, where c is the speed of light.
    • Substituting this into Planck’s equation gives E = hc/λ.
  • Wave Number (1/λ):
    • The wave number is the reciprocal of the wavelength.
    • It represents the number of waves per unit length.
    • Energy is therefore inversely proportional to wavelength, and directly proportional to wave number and frequency.
  • Significance: Planck’s theory laid the foundation for quantum mechanics, explaining phenomena like blackbody radiation and the photoelectric effect.

2.3 Bohr’s Atomic Theory: Quantized Orbits

2.3.1 Describe Bohr’s atomic theory;

• • Postulates:
    • Electrons revolve around the nucleus in specific, circular orbits called stationary states.
    • Electrons in these orbits do not radiate energy.
    • Electrons can transition between orbits by absorbing or emitting photons of energy equal to the energy difference between the orbits.
    • The angular momentum of an electron in an orbit is quantized (mvr = nh/2π).

2.3.2 Calculate the radius and energy of revolving electrons in orbits with reference to Bohr’s atomic theory;

• • Radius (r_n):
    • r_n = n² x a⁰, where:
      • n is the principal quantum number (n = 1, 2, 3…).
      • a⁰ is the Bohr radius (52.9 pm).
  • Energy (En):
    • E_n = -Rh(1/n₂), where:
      • Rh is the Rydberg constant (2.18 x 10^-18 J).
      • The negative sign indicates that the electron is bound to the nucleus.

2.3.3 Explain spectral lines of hydrogen atom;

• • Electron Transitions: When an electron transitions from a higher energy level (n₂) to a lower energy level (n₁), it emits a photon of energy equal to the difference between the two levels (ΔE = E₂ – E₁).
  • Spectral Series: The emitted photons correspond to specific wavelengths, creating spectral lines. The hydrogen spectrum consists of series like:

    

    • Lyman (n = 1): Ultraviolet region.
    • Balmer (n = 2): Visible region.
    • Paschen (n = 3): Infrared region.

2.3.4 Calculate wave numbers of photons of various spectral series with reference to Bohr’s atomic theory;

• • Rydberg Equation: 1/λ = Rh (1/n₁² – 1/n₂²), where Rh is the Rydberg constant.

2.3.5 Discuss the defects of Bohr’s atomic theory;

• • Multi-electron atoms: It fails to explain the spectra of atoms with more than one electron.
  • Zeeman and Stark effects: It cannot explain the splitting of spectral lines in magnetic (Zeeman effect) and electric (Stark effect) fields.
  • Wave-particle duality: It treats electrons as particles, ignoring their wave nature.
  • Heisenberg’s uncertainty principle: It violates the uncertainty principle by assuming electrons have definite positions and momenta.
  • Fine structure: It does not account for the fine structure of spectral lines.

2.4 X-Rays and Atomic Numbers: Moseley’s Contribution

2.4.1 Define ‘X-rays’;

• • X-rays are high-energy electromagnetic radiation with short wavelengths, produced when rapidly moving electrons collide with a metal target.

2.4.2 Explain the production and uses of X-rays;

• • Production: Electrons are accelerated by a high voltage and strike a metal target (anode). The rapid deceleration of electrons causes them to emit X-rays.
  • Uses:
    • Medical imaging: Radiography, CT scans.
    • Crystallography: Determining crystal structures.
    • Industrial inspection: Detecting flaws in materials.
    • Security: airport scanners.

2.4.3 Describe the relationship between X-ray frequency and atomic number of different elements with reference to Moseley’s experiment;

• • Moseley’s experiment showed that the frequency of characteristic X-rays emitted by an element is directly related to its atomic number.

2.4.4 State Moseley’s law and its significance;

• • Moseley’s Law: √ν ∝ Z (where ν is the frequency of X-rays and Z is the atomic number).
  • Significance:
    • Confirmed that the atomic number is a more fundamental property of an element than its atomic mass.
    • Provided a more accurate and logical arrangement of elements in the periodic table.
    • Helped in the discovery of missing elements.

2.5 Heisenberg’s Uncertainty Principle and Quantum Numbers