Atomic Structure Practice Flashcards

Discovery of Subatomic Particles and Fundamental Experiments

Understanding Subatomic Particles
- Subatomic particles are the fundamental entities that reside inside the atom and constitute its internal structure.
- Historical Context: John Dalton originally proposed that atoms were indivisible, the smallest units of matter. However, subsequent experimental evidence demonstrated that atoms are actually composed of smaller constituents: electrons, protons, and neutrons.
The Gas Discharge Tube Experiment
- Purpose: This experiment was pivotal in revealing the existence of subatomic particles.
- Experimental Setup:
  - Mechanism: A sealed glass tube (known as a gas discharge tube).
  - Components: Two metal electrodes (cathode and anode) connected to a high-voltage power source.
  - Conditions: A low-pressure environment, specifically created at approximately $10^{-6}\,atm$ .
  - Trigger: Initial ionization is achieved using Ultraviolet (UV) light or cosmic rays.
- The Process:
  1. Ionization: Neutral gas atoms within the tube are ionized, resulting in the creation of positive gas ions and free electrons.
  2. Acceleration: These charged particles accelerate rapidly due to the influence of the applied electric field.
  3. Collision: Positive ions impact the cathode, which triggers the release of electrons.
  4. Detection: The movement of these particles is monitored and observed through various detection methods.
Cathode Rays
- Definition: A stream of negatively charged particles that originate at the cathode and travel toward the anode.
- Key Properties:
  - They travel in perfectly straight lines, evidenced by their ability to cast sharp shadows of objects in their path.
  - They exhibit deflection when subjected to both electric and magnetic fields.
  - They carry an inherent negative charge.
  - They possess the ability to produce fluorescence and phosphorescence.
- Historical Clarification: While J.J. Thomson is often associated with electron discovery, the term "Cathode Rays" was actually named by E. Goldstein.
Anode Rays (Canal Rays)
- Definition: A stream of positively charged gas ions that travel between the electrodes.
- Properties:
  - They originate in the region between the electrodes and move toward the cathode.
  - They are composed of positive gas ions.
  - Like cathode rays, they are deflected by electric and magnetic fields, but in the opposite direction.
  - They travel in a direction strictly opposite to that of cathode rays.
Experimental Refinements
- Perforated Electrodes: These are electrodes manufactured with small holes to permit the passage of particles.
- Detection Materials: Zinc sulfide ( $ZnS$ ) screens are placed behind the electrodes. Zinc sulfide is a scintillator that demonstrates phosphorescence.
- Phosphorescence vs. Fluorescence:
  - Phosphorescence: Characterized by delayed light emission; the glow continues even after the energy source is removed.
  - Fluorescence: characterized by immediate light emission; the glow stops the moment the energy source is removed.

Measurements of Charge-to-Mass Ratio and Electron Discovery

Deflection Experiments and Charge Confirmation
- Electric Field Deflection:
  - Cathode rays deflect toward the positive plate, confirming their negative charge.
  - Anode rays deflect toward the negative plate, confirming their positive charge.
- Magnetic Field Deflection: Both types of rays deflect according to the Lorentz force, moving in opposite directions due to their opposing charges.
- Balanced Fields: By balancing the electric and magnetic fields, researchers ensure particles travel in a straight line. This equilibrium state was used by J.J. Thomson to determine the charge-to-mass ( $e/m$ ) ratio.
J.J. Thomson's Landmark Experiment
- Achievement: He successfully measured the charge-to-mass ratio ( $e/m$ ) of cathode rays.
- Methodology: He applied simultaneous electric and magnetic fields to measure the resulting deflection.
- Significance: This proved that cathode rays consist of particles with a definite and measurable mass-to-charge identity, establishing that atoms are indeed divisible.
Fundamental Nature of the Electron
- Independence of Ratio: A critical discovery was that the $e/m$ ratio of cathode rays remains constant regardless of:
  1. The specific type of gas used inside the discharge tube.
  2. The material used to construct the cathode.
- This constancy proves that all materials and gases contain the same fundamental negatively charged particle.
Formal Discovery of the Electron
- J.J. Thomson initially referred to these particles as "corpuscles."
- G.J. Stoney: Renamed these particles "electrons" in 1874.
- Quantified Data:
  - Charge-to-mass ratio ( $e/m$ ): $-1.75 \times 10^{11}\,C/kg$ .
  - Fundamental charge of an electron ( $e$ ): $-1.60 \times 10^{-19}\,C$ .

Discovery of Protons, Neutrons, and the Millikan Oil Drop Experiment

Proton Discovery Nuances
- Anode rays are not fundamental particles. Their $e/m$ ratio depends entirely on the nature of the gas inside the tube and is significantly lower than that of electrons.
- Historical Credit:
  - E. Goldstein: Performed anode ray experiments but did not prove the existence of a fundamental particle (the proton).
  - Ernest Rutherford: Credited with the actual discovery of the proton in 1919 through the bombardment of nitrogen atoms with alpha particles.
- Rutherford’s 1919 Experiment:
  - Method: Bombarded nitrogen atoms with alpha ( $\alpha$ ) particles ( $2$ protons + $2$ neutrons).
  - Result: A hydrogen nucleus (a proton) was ejected from the nitrogen.
  - This confirmed Prout's Hypothesis ( $1813$ - $1814$ ), which suggested all elements are composed of hydrogen.
Neutron Discovery (James Chadwick, 1932)
- Method: Bombarded beryllium metal with alpha particles.
- Observation: Emission of neutral radiation that was NOT gamma ( $\gamma$ ) rays.
- Detection: When this radiation struck paraffin wax, protons were ejected.
- Conclusion: Since massless gamma photons were too light to eject protons, the radiation must consist of massive neutral particles, which Chadwick named "neutrons."
The Millikan Oil Drop Experiment
- Purpose: To determine the fundamental unit of electric charge.
- Setup:
  - An oil atomizer creates a fine mist of oil droplets.
  - X-rays ionize the air, producing positive ions and electrons.
  - Electrons attach to the oil droplets, giving them a negative charge.
  - An electric field is applied between two horizontal plates.
- The Suspension Principle:
  - Downward force (Gravity): $F_g = mg$ .
  - Upward force (Electric): $F_e = qE.\n - Balance condition for suspension: mg = qE.\n - **Findings**:\n - Fundamental electron charge (e $):$ -1.60 \times 10^{-19}\,C.\n - Charge is quantized; all observed charges are integer multiples of this value.\n - Electron mass calculation (m = e / (e/m) $):$ \frac{-1.60 \times 10^{-19}}{-1.75 \times 10^{11}} = 9.11 \times 10^{-31}\,kg.\n\n# Comparative Properties of Subatomic Particles\n\n- **Mass and Charge Table**:\n - **Electron (e)**:\n - Charge: -1.60 \times 10^{-19}\,C.\n - Relative Charge: -1.\n - Mass: 9.11 \times 10^{-31}\,kg.\n - **Proton (p)**:\n - Charge: +1.60 \times 10^{-19}\,C.\n - Relative Charge: +1.\n - Mass: 1.67 \times 10^{-27}\,kg.\n - **Neutron (n)**:\n - Charge: 0\,C.\n - Relative Charge: 0.\n - Mass: 1.67 \times 10^{-27}\,kg $(Slightly heavier than the proton due to quark composition:$ 2 $down +$ 1 $up for neutrons vs.$ 2 $up +$ 1 down for protons).\n\n# Evolution of Atomic Models: Thomson and Rutherford\n\n- **Thomson’s Plum Pudding Model (1904)**\n - **The Concept**: Atoms consist of a positively charged sphere with electrons embedded uniformly within it, much like raisins in a pudding or seeds in a watermelon.\n - **Reasoning**: Atoms are electrically neutral, necessitating a positive charge to balance the negative electrons. At this time, protons had not been discovered.\n - **Key Implications**:\n - Mass is uniformly distributed throughout the atom.\n - Total positive charge equals total negative charge.\n - **Major Failures**:\n - It cannot explain the results of Rutherford's alpha scattering experiment.\n - It fails to define atomic stability because opposite charges in direct contact should create unbalanced forces.\n\n- **Rutherford’s Alpha Scattering Experiment**\n - **Setup**:\n - Source: Radium (alpha particle emitter) housed in a lead block with a small aperture.\n - Alpha Particles: Helium nuclei (2 $protons,$ 2 $neutrons) with a charge of$ +2 $and mass of$ 4.\n - Target: Gold foil, approximately 1000 atoms thick. Gold was chosen for its extreme malleability.\n - Detector: A movable silver-activated zinc sulfide screen (ZnS) used to observe scintillations.\n - **Observations**:\n 1. Most alpha particles passed through the foil without any deviation.\n 2. Some particles were deflected at small angles.\n 3. Approximately 1 $in every$ 10,000 $-$ 20,000 $particles retraced their path ($ 180^{\circ} deflection).\n - **Conclusions**:\n - Most of the atom is empty space.\n - The entire mass and positive charge are concentrated in a tiny, dense central region called the **nucleus**.\n - The nucleus is positively charged (explaining the repulsion of positive alpha particles).\n\n- **Rutherford’s Nuclear Model (The Planetary Model)**\n - **Features**:\n - A positively charged nucleus sits at the center.\n - Electrons revolve around the nucleus in circular orbits, similar to planets orbiting the sun.\n - The volume of the nucleus is infinitesimal compared to the total volume of the atom (Analogy: a cricket ball in a cricket ground).\n - **Drawbacks (Maxwell’s Objection)**:\n - According to classical electromagnetism, a charged particle (the electron) moving in a circular path is accelerating.\n - Accelerated charges must continuously emit electromagnetic radiation.\n - This energy loss would cause the electron to spiral into the nucleus, making the atom unstable. Real atoms, however, are stable.\n\n# Atomic Number, Mass Number, and Isotopes\n\n- **Fundamental Variables**\n - **Atomic Number (Z)**: The number of protons in the nucleus. In a neutral atom, this also equals the number of electrons.\n - **Mass Number (A)**: The total number of protons and neutrons (collectively called nucleons) in the nucleus.\n - **Formula**: A = Z + N $(where$ N is the number of neutrons).\n - **Representation**: {^{A}{Z}X} $(e.g., carbon-12 is written as$ {^{12}{6}C}).\n\n- **Practice Calculation: Bromine ({^{80}{35}Br})**\n - Protons: 35 (Atomic number).\n - Electrons: 35 (Neutral atom).\n - Neutrons: 80 - 35 = 45.\n\n- **Isotopes and Isobars**\n - **Isotopes**: Atoms of the same element (Z $is the same) with different mass numbers ($ A $is different). They possess different numbers of neutrons. Example:$ {^{35}{17}Cl} $and$ {^{37}{17}Cl}.\n - **Isobars**: Atoms of different elements (different Z $) that have the same mass number ($ A $). Example:$ {^{40}{18}Ar} $and$ {^{40}{20}Ca}.\n\n# Electromagnetic Radiation and Wave Characteristics\n\n- **Types of Waves**\n - **Mechanical Waves**: Require a material medium to travel (e.g., sound waves, water waves).\n - **Electromagnetic (EM) Waves**: Do not require a medium and can travel through a vacuum at the speed of light (c = 3.00 \times 10^{8}\,m/s).\n\n- **Maxwell’s Electromagnetic Theory**\n - Accelerated charged particles produce oscillating electric and magnetic fields.\n - These fields are perpendicular to each other and perpendicular to the direction of wave propagation.\n\n- **Wave Parameters**\n - **Amplitude (A)**: Maximum displacement from the mean position.\n - **Frequency (\nu $)**: Number of waves passing a point in one second ($ Hz $or$ s^{-1}).\n - **Wavelength (\lambda $)**: Distance between consecutive crests or troughs ($ m).\n - **Wave Number (\bar{ u} $)**: Reciprocal of wavelength ($ \bar{ u} = \frac{1}{\lambda} $). Common unit:$ cm^{-1}.\n - **Time Period (T $)**: Time for one wave cycle ($ T = \frac{1}{\nu}).\n - **Speed (c $)**: For all EM waves in vacuum,$ c = \nu \times \lambda = 3.00 \times 10^{8}\,m/s.\n\n- **Electromagnetic Spectrum Trends**\n - From Radio waves to Gamma rays:\n - Wavelength decreases.\n - Frequency increases.\n - Penetrating power and energy increase.\n - **Order**: Radio > Microwave > Infrared > Visible (VIBGYOR) > Ultraviolet > X-ray > Gamma ray.\n\n# Planck’s Quantum Theory and Black Body Radiation\n\n- **The Failure of Wave Theory**\n - Classical wave theory could not explain Black Body Radiation, the Photoelectric Effect, the variation of heat capacity of solids, or line spectra.\n\n- **Black Body Radiation**\n - **Definition**: A black body is an ideal body that absorbs and emits all frequencies of radiation.\n - **Observation**: As temperature increases, the intensity of radiation increases and the peak wavelength shifts toward the blue (shorter wavelength) end of the spectrum. Classical physics predicted intensity would increase infinitely at short wavelengths (the "ultraviolet catastrophe"), which was not observed.\n\n- **Planck’s Postulates**\n - Energy is not absorbed or emitted continuously, but in discrete packets called **quanta** (singular: quantum). For light, these are **photons**.\n - The energy of a quantum is directly proportional to its frequency: E = h \times \nu.\n - **Planck’s Constant (h $)**:$ 6.626 \times 10^{-34}\,J \cdot s.\n - Total energy for n $quanta:$ E = n \times h \times \nu $, where$ n is a whole number (quantization).\n\n# The Photoelectric Effect\n\n- **Discovery (Hertz, 1887)**\n - When light of a sufficient frequency strikes a metal surface, electrons are ejected immediately. \n\n- **Key Observations**:\n 1. **Immediate Ejection**: There is no time lag between the light striking and the electron being ejected.\n 2. **Threshold Frequency (\nu_0)**: There is a minimum frequency below which no electrons are ejected, regardless of the light's intensity.\n 3. **Intensity Relationship**: The number of ejected electrons (photoelectric current) is proportional to the intensity (brightness) of light.\n 4. **Kinetic Energy Relationship**: The kinetic energy of the ejected electrons depends on the frequency of the light, not its intensity.\n\n- **Einstein’s Photoelectric Equation**\n - Energy of incident photon = Work function + Kinetic Energy of electron.\n - h\nu = h\nu_0 + \frac{1}{2}mv^{2}.\n - **Work Function (\phi $)**: The minimum energy required to eject an electron ($ \phi = h\nu_0).\n\n# Atomic Spectra and the Hydrogen Emission Spectrum\n\n- **Types of Spectra**\n - **Spectrum**: A band of radiations separated by a spectroscope (prism and detector).\n - **Continuous Spectrum**: Colors overlap with no clear boundaries (e.g., white light spectrum).\n - **Emission Spectrum**: Produced when radiation from an excited source is analyzed. Appears as bright lines on a dark background.\n - **Absorption Spectrum**: Produced when white light passes through a substance before being analyzed. Appears as dark lines on a continuous bright background.\n\n- **Line Spectrum of Hydrogen**\n - When high voltage is applied to hydrogen gas at low pressure, it emits blue light. Analysis reveals specific spectral series:\n - **Lyman Series**: Transitions to n_1 = 1 (Ultraviolet region).\n - **Balmer Series**: Transitions to n_1 = 2 (Visible region).\n - **Paschen Series**: Transitions to n_1 = 3 (Infrared region).\n - **Brackett Series**: Transitions to n_1 = 4 (Infrared region).\n - **Pfund Series**: Transitions to n_1 = 5 (Infrared region).\n\n- **Rydberg Equation**\n - Used to calculate the wavelength of any transition:\n - \frac{1}{\lambda} = R_H \left( \frac{1}{n{1}^{2}} - \frac{1}{n_{2}^{2}} \right).\n - **Rydberg Constant (R_H $)**:$ 109,677\,cm^{-1}.\n - Condition: n_2 > n_1.\n\n# Bohr’s Atomic Model\n\n- **Key Postulates (1913)**\n 1. **Stationary States**: Electrons revolve in specific circular orbits of fixed radius and energy (n = 1, 2, 3… $or$ K, L, M, N…).\n 2. **Energy Conservation**: As long as an electron stays in a stationary orbit, it does not radiate energy, overcoming Maxwell’s objection.\n 3. **Angular Momentum Quantization**: Electrons can only exist in orbits where their angular momentum is an integral multiple of \frac{h}{2\pi} $:$ mvr = \frac{nh}{2\pi}.\n 4. **Transitions**: Energy changes only occur when an electron jumps between orbits. \Delta E = E_{higher} - E_{lower} = h\nu.\n\n- **Mathematical Results for Hydrogen**\n - **Energy (E_n $)**:$ E_n = -13.6 \times \frac{Z^{2}}{n^{2}}\,eV.\n - **Radius (r_n $)**:$ r_n = 0.529 \times \frac{n^{2}}{Z}\,\text{\AA}.\n - **Bohr Radius (a_0 $)**: The radius of the first orbit of hydrogen ($ n=1, Z=1 $), which is$ 0.529\,\text{\AA} $or$ 52.9\,pm.\n\n- **Drawbacks**:\n - Fails for multi-electron atoms.\n - Cannot explain the splitting of spectral lines in magnetic (Zeeman Effect) or electric (Stark Effect) fields.\n - Violates both de Broglie’s hypothesis and Heisenberg’s Uncertainty Principle.\n\n# Quantum Mechanical Framework\n\n- **de Broglie’s Hypothesis (1924)**\n - Matter, like light, exhibits wave-particle duality. For any moving particle:\n - \lambda = \frac{h}{mv} = \frac{h}{p}.\n - Macroscopic objects have such high mass that their wavelength is too small to observe.\n\n- **Heisenberg’s Uncertainty Principle (1927)**\n - It is impossible to simultaneously determine the exact position and momentum of a microscopic particle.\n - \Delta x \times \Delta p \ge \frac{h}{4\pi}.\n - \Delta x \times m\Delta v \ge \frac{h}{4\pi}.\n\n- **Schrödinger Wave Equation (1926)**\n - The fundamental equation of quantum mechanics describing electron wave-motion:\n - \hat{H}\psi = E\psi.\n - **\psi (Wave function)**: Represents the amplitude of the electron wave. It can be positive or negative.\n - **\psi^{2} (Probability Density)**: The square of the wave function is always positive and represents the probability of finding an electron at a specific point in 3D space.\n\n# Orbitals and Quantum Numbers\n\n- **Orbit vs. Orbital**\n - **Orbit**: A well-defined 2D circular path (Bohr).\n - **Orbital**: A 3D region around the nucleus where the probability of finding an electron is maximum (approx. 90\%).\n\n- **The Four Quantum Numbers**\n 1. **Principal Quantum Number (n $)**: Indicates the main energy level/shell ($ 1, 2, 3…). Determines the size and energy.\n 2. **Azimuthal (Subsidiary) Quantum Number (l $)**: Indicates the shape of the subshell. Values:$ 0 $to$ (n-1).\n - l=0: s subshell (spherical)\n - l=1: p subshell (dumbbell)\n - l=2: d subshell (complex/double-dumbbell)\n - l=3: f subshell (complex)\n 3. **Magnetic Quantum Number (m $)**: Indicates the orientation of the orbital in space. Values:$ -l $to$ +l $(total of$ 2l+1 values).\n 4. **Spin Quantum Number (s $)**: Indicates the direction of electron spin ($ +\frac{1}{2} $for up-spin,$ -\frac{1}{2} for down-spin).\n\n- **Shapes and Nodes**\n - **s Orbital**: Spherical. High probability near the nucleus. Only radial nodes (n-1 total nodes).\n - **p Orbital**: Dumbbell-shaped with three orientations: p_x, p_y, p_z. Each has one angular node (nodal plane).\n - **d Orbital**: Five orientations: d_{xy}, d_{yz}, d_{zx}, d_{x^{2}-y^{2}}, d_{z^{2}}. Each has two angular nodes.\n - **Nodes**: Regions of zero probability.\n - Radial nodes = n - l - 1.\n - Angular nodes = l.\n - Total nodes = n - 1.\n\n# Electronic Configuration Rules\n\n- **Aufbau Principle**: Electrons occupy orbitals in order of increasing energy. Filling follows the (n+l) $rule. If two orbitals have the same$ (n+l) $, the one with the lower$ n fills first.\n - Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p…\n\n- **Pauli Exclusion Principle**: No two electrons in an atom can have the same set of four quantum numbers. This means an orbital can hold a maximum of two electrons, and they must have opposite spins.\n\n- **Hund’s Rule of Maximum Multiplicity**: In degenerate orbitals (orbitals with same energy), pairing occurs only after every orbital in the subshell is singly occupied with parallel spins. This maximizes stability through exchange energy and symmetry.\n\n- **Exceptional Configurations**\n - **Chromium (Z=24 $)**: Expected$ [Ar]4s^{2}3d^{4} $, Actual$ [Ar]4s^{1}3d^{5}.\n - **Copper (Z=29 $)**: Expected$ [Ar]4s^{2}3d^{9} $, Actual$ [Ar]4s^{1}3d^{10}.\n - **Reasoning**: Half-filled (d^5 $) and fully-filled ($ d^{10} $) subshells are extra stable due to symmetrical distribution and high exchange energy. Number of exchanges for$ d^5 = \frac{5 \times (5-1)}{2} = 10.\n\n- **Mnemonic for Period 4 Transition Elements**:\n - "Sweetie Tiwari Vijay Chauhan, Mango Fir Continental Nigerian Quiz"\n - Elements: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn$$.