Class 12 Physics Notes Chapter 4 (Atoms) – Physics Part-II Book

Detailed Notes with MCQs of Chapter 4, 'Atoms', from your NCERT Physics Part-II textbook. This is a fundamental chapter, and understanding atomic structure is crucial not just for your board exams but also for various government exams where Physics is a component. We'll break down the key concepts systematically.

Chapter 4: Atoms - Detailed Notes for Exam Preparation

1. Introduction: Early Models

• Atoms are the fundamental building blocks of matter. Understanding their structure evolved over time through various models.
• Dalton's Atomic Theory (Recap): Atoms are indivisible (later proven wrong).
• Thomson's Model (Plum Pudding Model - approx. 1898):
  • Proposed by J.J. Thomson after discovering the electron.
  • Concept: Atom is a sphere of positive charge with negatively charged electrons embedded in it, like plums in a pudding or seeds in a watermelon.
  • The total positive charge equals the total negative charge, making the atom electrically neutral.
  • Limitation: Could not explain the results of the alpha-scattering experiment.

2. Rutherford's Alpha-Scattering Experiment (Geiger-Marsden Experiment - approx. 1911)

• Setup: A narrow beam of alpha particles (Helium nuclei, He²⁺) from a radioactive source (like Bismuth-214) was directed towards a thin gold foil. A zinc sulfide (ZnS) screen detected the scattered alpha particles.
• Observations:
  • Most alpha particles passed straight through the foil undeflected.
  • A small fraction (about 1 in 8000) were deflected by small angles.
  • A very few (about 1 in 20,000) were deflected by large angles (more than 90°), some even bounced back (180° deflection).
• Conclusions:
  • Most space in an atom is empty: (As most particles passed straight).
  • Positive charge is concentrated: The positive charge and most of the atom's mass are concentrated in a very small central region called the nucleus. (Explains large-angle scattering due to strong electrostatic repulsion).
  • Electrons revolve around the nucleus: Electrons orbit the nucleus like planets around the sun.
• Impact Parameter (b): The perpendicular distance of the initial velocity vector of the alpha particle from the center of the nucleus. Scattering angle (θ) depends on 'b'. Smaller 'b' leads to larger 'θ'. For head-on collision (b=0), θ = 180°.
• Distance of Closest Approach (r₀): For head-on collision, the alpha particle stops momentarily and returns. At this point, its initial kinetic energy is completely converted into electrostatic potential energy.
  • K.E. = (1/4πε₀) * (Ze)(2e) / r₀ => r₀ = (1/4πε₀) * (2Ze²) / K.E. (where Ze is nuclear charge, 2e is alpha particle charge). This gives an estimate of the nucleus size (~10⁻¹⁴ to 10⁻¹⁵ m).

3. Rutherford's Nuclear Model (Planetary Model)

• Concept: Atom consists of a tiny, dense, positively charged nucleus at the center, and negatively charged electrons revolve around it in circular orbits. Electrostatic force provides the necessary centripetal force.
• Limitations:
  • Instability: According to classical electromagnetic theory, an accelerating charged particle (like an electron in orbit) must radiate energy continuously. This would cause the electron to spiral into the nucleus, making the atom unstable. (Atoms are stable!).
  • Inability to Explain Line Spectra: If electrons lose energy continuously, they should emit radiation of all frequencies, leading to a continuous spectrum. However, atoms emit discrete line spectra.

4. Bohr's Model of the Hydrogen Atom (1913)

• Applied to hydrogen and hydrogen-like atoms (single electron species like He⁺, Li²⁺).

• Combined classical physics with early quantum concepts.

• Bohr's Postulates:

  1. Stable Orbits: Electrons revolve around the nucleus only in certain specific, non-radiating orbits called stationary orbits. The electrostatic force provides the centripetal force.
     mv²/r = (1/4πε₀) * Ze²/r²
  2. Quantization of Angular Momentum: An electron can revolve only in those orbits for which its angular momentum (L = mvr) is an integral multiple of h/2π (where 'h' is Planck's constant).
     L = mvr = n(h/2π), where n = 1, 2, 3,... is the principal quantum number.
  3. Frequency Condition: An atom radiates energy only when an electron jumps from a higher energy orbit (Eᵢ) to a lower energy orbit (E<0xE2><0x82><0x93>). The frequency (ν) of the emitted photon is given by:
     hν = Eᵢ - E<0xE2><0x82><0x93>
     Energy is absorbed for a jump from a lower to a higher orbit.

• Derivations & Key Results (for Hydrogen-like atoms, charge Ze):

  • Radius of nth orbit (r<0xE2><0x82><0x99>): r<0xE2><0x82><0x99> = (n²h²ε₀) / (πmZe²).
    • r<0xE2><0x82><0x99> ∝ n²/Z.
    • For Hydrogen (Z=1), radius of the first orbit (n=1) is called Bohr radius (a₀): a₀ ≈ 0.529 Å = 0.0529 nm.
    • r<0xE2><0x82><0x99> = n² a₀ (for Hydrogen).
  • Velocity of electron in nth orbit (v<0xE2><0x82><0x99>): v<0xE2><0x82><0x99> = (Ze²) / (2nhε₀).
    • v<0xE2><0x82><0x99> ∝ Z/n.
  • Energy of electron in nth orbit (E<0xE2><0x82><0x99>):
    • Kinetic Energy (K<0xE2><0x82><0x99>): (1/2)mv² = (1/8πε₀) * (Ze²/r<0xE2><0x82><0x99>)
    • Potential Energy (U<0xE2><0x82><0x99>): -(1/4πε₀) * (Ze²/r<0xE2><0x82><0x99>)
    • Total Energy (E<0xE2><0x82><0x99>): K<0xE2><0x82><0x99> + U<0xE2><0x82><0x99> = -(1/8πε₀) * (Ze²/r<0xE2><0x82><0x99>) = -(mZ²e⁴) / (8n²h²ε₀²).
    • E<0xE2><0x82><0x99> ∝ -Z²/n². The negative sign indicates the electron is bound to the nucleus.
    • For Hydrogen (Z=1): E<0xE2><0x82><0x99> = -13.6 / n² eV.
    • Ground State (n=1): Lowest energy state. E₁ = -13.6 eV for Hydrogen.
    • Excited States (n=2, 3, ...): Higher energy states.
    • Ionization Energy: Minimum energy required to remove an electron from the ground state to infinity (n=∞, E=0). For Hydrogen, Ionization Energy = 0 - E₁ = 13.6 eV.
    • Excitation Energy: Energy required to move an electron from the ground state to an excited state.

• Successes of Bohr's Model:

  • Explained the stability of atoms.
  • Successfully explained the observed line spectrum of hydrogen and hydrogen-like ions.
  • Provided accurate calculations for energies and radii in hydrogen-like atoms.

• Limitations of Bohr's Model:

  • Applicable only to single-electron atoms (failed for multi-electron atoms).
  • Could not explain the fine structure (splitting of spectral lines into closely spaced lines).
  • Could not explain the relative intensities of spectral lines.
  • Could not explain the Zeeman effect (splitting of spectral lines in a magnetic field) and Stark effect (splitting in an electric field).
  • Violated Heisenberg's Uncertainty Principle (assumes definite position and momentum simultaneously).
  • Could not explain how atoms combine to form molecules.

5. Atomic Spectra

• When atoms are excited (e.g., by heating or electric discharge), electrons jump to higher energy levels. When they return to lower levels, they emit photons of specific frequencies/wavelengths, forming an emission spectrum.

• When white light passes through a cool gas, atoms absorb photons of specific frequencies corresponding to possible electron transitions, resulting in dark lines in the spectrum, called an absorption spectrum.

• Spectral Series of Hydrogen: The emission spectrum consists of distinct series of lines. The wavelength (λ) or wave number (ν̄ = 1/λ) of emitted photons is given by the Rydberg formula:
  1/λ = R Z² (1/n<0xE2><0x82><0x93>² - 1/nᵢ²)
  Where:

  • R is the Rydberg constant ≈ 1.097 × 10⁷ m⁻¹.
  • n<0xE2><0x82><0x93> is the principal quantum number of the final (lower energy) orbit.
  • nᵢ is the principal quantum number of the initial (higher energy) orbit (nᵢ > n<0xE2><0x82><0x93>).
  • For Hydrogen, Z=1.

  Series Name	Final Orbit (n<0xE2><0x82><0x93>)	Initial Orbit (nᵢ)	Spectral Region
  Lyman	1	2, 3, 4, ...	Ultraviolet
  Balmer	2	3, 4, 5, ...	Visible
  Paschen	3	4, 5, 6, ...	Infrared
  Brackett	4	5, 6, 7, ...	Infrared
  Pfund	5	6, 7, 8, ...	Far Infrared

• Series Limit: The shortest wavelength (highest energy) line in a series, corresponding to a transition from nᵢ = ∞.

6. de Broglie's Explanation of Bohr's Second Postulate

• Louis de Broglie proposed that electrons (like other matter particles) exhibit wave-like properties with wavelength λ = h/p = h/mv.
• He suggested that an electron in a stationary orbit behaves like a standing wave. For a standing wave to form around the circumference of an orbit, the circumference must be an integral multiple of the electron's wavelength.
  2πr<0xE2><0x82><0x99> = nλ (where n = 1, 2, 3, ...)
• Substituting λ = h/mv:
  2πr<0xE2><0x82><0x99> = n(h/mv)
  Rearranging gives: mvr<0xE2><0x82><0x99> = n(h/2π)
• This is precisely Bohr's second postulate (quantization of angular momentum). It provides a physical basis for the postulate based on the wave nature of the electron.

Key Formulas for Quick Revision:

• Distance of Closest Approach: r₀ = (1/4πε₀) * (2Ze²) / K.E.
• Bohr's Angular Momentum Quantization: mvr = n(h/2π)
• Bohr's Frequency Condition: hν = Eᵢ - E<0xE2><0x82><0x93>
• Radius of nth Orbit: r<0xE2><0x82><0x99> ∝ n²/Z ; r<0xE2><0x82><0x99> = n² a₀ (H atom)
• Velocity in nth Orbit: v<0xE2><0x82><0x99> ∝ Z/n
• Energy in nth Orbit: E<0xE2><0x82><0x99> ∝ -Z²/n² ; E<0xE2><0x82><0x99> = -13.6 Z²/n² eV
• Rydberg Formula: 1/λ = R Z² (1/n<0xE2><0x82><0x93>² - 1/nᵢ²)
• de Broglie Wavelength: λ = h/mv
• de Broglie's condition for stable orbit: 2πr = nλ

Remember to focus on the postulates, the successes and limitations of each model, the formulas for radius, velocity, and energy in Bohr's model, and the different spectral series of hydrogen.

Multiple Choice Questions (MCQs)

Here are 10 MCQs based on the 'Atoms' chapter for your practice:

1. Rutherford's alpha-scattering experiment led to the conclusion that:
   a) Atoms are indivisible.
   b) The positive charge and mass are uniformly distributed throughout the atom.
   c) The entire positive charge and most of the mass are concentrated in a tiny central core.
   d) Electrons are embedded in a sphere of positive charge.

2. According to Bohr's model, the angular momentum of an electron in the 3rd orbit of a hydrogen atom is:
   a) h/2π
   b) 3h/π
   c) 3h/2π
   d) h/3π

3. The energy of an electron in the ground state (n=1) of a hydrogen atom is -13.6 eV. What is its energy in the first excited state (n=2)?
   a) -6.8 eV
   b) -3.4 eV
   c) -1.51 eV
   d) -13.6 eV

4. The spectral series of the hydrogen atom that lies in the visible region of the electromagnetic spectrum is:
   a) Lyman series
   b) Balmer series
   c) Paschen series
   d) Pfund series

5. If r<0xE2><0x82><0x99> is the radius of the nth orbit in Bohr's model, then the radius of the (n+1)th orbit will be proportional to:
   a) n²
   b) 1/n²
   c) (n+1)²
   d) 1/(n+1)²

6. The minimum energy required to remove an electron from a hydrogen atom in its ground state is called:
   a) Excitation energy
   b) Kinetic energy
   c) Binding energy
   d) Ionization energy

7. Which of the following could not be explained by Rutherford's atomic model?
   a) Existence of a nucleus
   b) Most space in an atom is empty
   c) Stability of atoms
   d) Scattering of alpha particles

8. According to de Broglie's hypothesis, Bohr's stationary orbits are those where the circumference of the orbit is:
   a) An integral multiple of the electron's de Broglie wavelength.
   b) Equal to the electron's de Broglie wavelength.
   c) Half an integral multiple of the electron's de Broglie wavelength.
   d) Inversely proportional to the electron's de Broglie wavelength.

9. The ratio of the radii of the first three Bohr orbits for hydrogen is:
   a) 1 : 2 : 3
   b) 1 : 1/2 : 1/3
   c) 1 : 4 : 9
   d) 1 : 8 : 27

10. The transition of an electron from n=4 to n=2 in a hydrogen atom results in the emission of a photon belonging to the:
    a) Lyman series (UV)
    b) Balmer series (Visible)
    c) Paschen series (IR)
    d) Brackett series (IR)

Answer Key:

1. c)
2. c) (L = nh/2π, n=3)
3. b) (E₂ = -13.6 / 2² = -13.6 / 4 = -3.4 eV)
4. b)
5. c) (r ∝ n², so for n+1, r ∝ (n+1)²)
6. d)
7. c)
8. a)
9. c) (r ∝ n², so r₁:r₂:r₃ = 1²:2²:3² = 1:4:9)
10. b) (Final orbit n<0xE2><0x82><0x93>=2 corresponds to Balmer series)

Study these notes thoroughly. Pay attention to the concepts behind the formulas and the limitations of the models. Good luck with your preparation!