Board exam focus — Atoms (CBSE & HBSE)

CBSE focuses on Rutherford's scattering experiment and model limitations, all four Bohr's postulates, derivation of radii and energy levels, and hydrogen spectrum series. HBSE emphasizes Bohr's model, energy level diagram, hydrogen spectral series classification, and numericals on energy and wavelength.

Rutherford and Bohr's Model of Atom

Thomson's Model (Plum Pudding)

Atom = sphere of positive charge with electrons embedded like plums in pudding. Failed: Could not explain large-angle scattering.

Rutherford's Scattering Experiment (1909–1911)

Setup: α-particles (He nuclei, charge +2e) aimed at thin gold foil (thickness ~100 nm).

Observations:

1. Most α-particles passed straight through
2. Some deflected by small angles
3. Very few (~1 in 10,000) deflected by >90°
4. Some bounced almost straight back (180°)

Conclusions (Rutherford's Nuclear Model):

1. Atom is mostly empty space
2. All positive charge and most mass concentrated in tiny nucleus (radius ~10⁻¹⁴ m)
3. Electrons revolve around nucleus
4. Nuclear size: ~10⁻¹⁵ m; Atomic size: ~10⁻¹⁰ m (ratio ~10⁵)

Limitations of Rutherford's Model

1. Spiral collapse: Accelerating electrons radiate energy → spiral into nucleus in ~10⁻⁸ s
2. Continuous spectrum: Should emit all frequencies, but atoms emit only discrete spectral lines

Bohr's Model (1913)

Niels Bohr modified Rutherford's model with quantum theory.

Bohr's Postulates

1. Stable orbits: Electrons revolve in certain allowed circular orbits without emitting radiation. These are stationary states.

1. Quantization condition: Angular momentum is quantized:

L = mvr = nℏ = nh/(2π) (n = 1, 2, 3, ...)

1. Energy emission/absorption: Electrons jump between orbits by emitting/absorbing a photon:

hν = E_i − E_f (emission); hν = E_f − E_i (absorption)

1. (Implicit) Coulomb's force provides centripetal force:

ke²/r² = mv²/r

Bohr's Derivations

Orbital radius: r_n = n²a₀ = n²×0.529 Å (a₀ = Bohr radius = 0.529 Å for hydrogen)

Orbital velocity: v_n = e²/(4πε₀nℏ) = c/137n (c = speed of light)

Energy of nth orbit: E_n = −13.6/n² eV

• n=1 (ground state): E₁ = −13.6 eV
• n=2: E₂ = −3.4 eV
• n=3: E₃ = −1.51 eV
• n=∞: E_∞ = 0 (ionized)

Ionization energy of hydrogen: 13.6 eV (from ground state)

Diagram Indicator: [Rutherford's α-scattering diagram showing most particles going straight, some deflecting, few bouncing back; also Bohr model circles with n=1,2,3,4 orbits with radii labeled and energy values.]

Atomic Spectra and Hydrogen Spectrum

Atomic Spectra

When atoms emit/absorb light, they do so at specific discrete wavelengths forming a line spectrum (characteristic of each element).

Emission spectrum: Bright lines on dark background (gas excited and emitting) Absorption spectrum: Dark lines on bright background (gas absorbs from white light)

Spectral Series of Hydrogen

Electrons jumping from higher to lower orbits emit photons. Different series correspond to different final orbit n_f:

Memory tip: LP PBP (Lyman → Paschen → Brackett → Pfund going outward)

Rydberg Formula

The wavelength λ of spectral lines of hydrogen:

1/λ = R_H[1/n_f² − 1/n_i²]

where R_H = Rydberg constant = 1.097×10⁷ m⁻¹

n_i > n_f (emission); n_i < n_f (absorption)

Important Lines

Energy Level Diagram

Energy levels E_n = −13.6/n² eV, n = 1, 2, 3, ...

Arrows pointing down = emission; up = absorption

All lines in same series converge at series limit (n_i → ∞).

Excitation vs Ionization:

• Excitation: Moving to higher orbit (Absorption, E > 0 from ground state to that level)
• Ionization: Complete removal from atom (E_ionization = 13.6 eV for ground state H)

Diagram Indicator: [Energy level diagram for hydrogen showing all n levels from 1 to ∞ on vertical axis with E in eV; arrows showing Lyman, Balmer, Paschen series; spectrum colors for Balmer series labeled.]

Energy Levels and Transitions

Energy Level Transitions

In quantum mechanics, electrons exist in stationary states with definite energies. Transitions between states follow strict rules.

Selection Rules and Transition Probabilities

• All transitions emit photons with E = hν = E_i − E_f
• Allowed transitions: Δn = any integer
• Forbidden transitions: Require special conditions
• Spontaneous emission vs Stimulated emission (LASER principle)

Hydrogen-like Atoms

For atoms with nuclear charge Z (single electron, like He⁺, Li²⁺):

r_n = n²a₀/Z E_n = −13.6Z²/n² eV ν = (R_H Z²c)[1/n_f² − 1/n_i²]

Examples:

• He⁺ (Z=2): E₁ = −13.6×4 = −54.4 eV
• Li²⁺ (Z=3): E₁ = −13.6×9 = −122.4 eV

Limitations of Bohr's Model

1. Works only for hydrogen-like atoms (one electron)
2. Cannot explain fine structure of spectral lines
3. Cannot explain relative intensities of spectral lines
4. Does not explain chemical bonding
5. Violates Heisenberg uncertainty principle (assumes exact r and v simultaneously)
6. Extended by Sommerfeld (elliptical orbits) and later quantum mechanics (Schrödinger equation)

Quantum Numbers (Introduction)

Schrödinger's wave equation for hydrogen gives:

• Principal quantum number n: Energy level (1, 2, 3, ...)
• Azimuthal quantum number l: Orbital shape (0 to n-1)
• Magnetic quantum number m_l: Orientation (−l to +l)
• Spin quantum number m_s: Electron spin (±1/2)

X-ray Emission

When high-energy electrons bombard metal:

1. Continuous X-rays (Bremsstrahlung): electrons decelerate, emit photons
2. Characteristic X-rays: Inner shell electrons knocked out → outer electrons fill vacancy → emit characteristic photons

Minimum wavelength (continuous): λ_min = hc/(eV)

LASER Principle

Light Amplification by Stimulated Emission of Radiation.

• Stimulated emission: Photon stimulates excited atom to emit identical photon
• Population inversion: More atoms in excited state than ground state
• Optical cavity: Mirrors cause light to amplify
• LASER light: Monochromatic, coherent, directional, intense

Diagram Indicator: [Detailed hydrogen energy level diagram showing all transitions with specific wavelengths labeled; arrows showing emission (downward) and absorption (upward) transitions; series boundaries marked.]

Frequently asked questions

Are these Atoms notes free?

Yes — the Atoms notes for Physics (Class 12) on Siksha Sarovar are completely free to read, with no account required.

Do these notes follow CBSE and HBSE?

Yes. The Atoms notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.

What does the Atoms chapter cover?

Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Atoms.