Structure of Atom
NIOS · Class 12 · Physics
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See them allState Bohr's quantization condition for angular momentum of an electron in an orbit.
Answer
Bohr's Quantization Condition: mvr = nh/2π Where: • m = mass of electron • v = speed of electron in orbit • r = radius of orbit • n = principal quantum number (n = 1, 2, 3, ...) • h = Planck's consta…
Calculate the radius of the first orbit (Bohr radius) of the hydrogen atom.
Answer
Formula: rₙ = n²h²ε₀ / (Ze²mπ) For hydrogen atom, Z = 1, n = 1: Given: • h = 6.626 × 10⁻³⁴ J·s • ε₀ = 8.85 × 10⁻¹² C² N⁻¹ m⁻² • e = 1.6 × 10⁻¹⁹ C • m = 9.11 × 10⁻³¹ kg Step 1: Substitute all values…
The energy of an electron in the nth orbit of hydrogen atom is −13.6/n² eV. Calculate the energy of an electron in the 3rd orbit.
Answer
Formula: Eₙ = −13.6/n² eV Given: n = 3 Step 1: Substitute n = 3 E₃ = −13.6 / (3)² Step 2: E₃ = −13.6 / 9 Step 3: E₃ = −1.51 eV Answer: Energy in 3rd orbit = −1.51 eV Key Insight: • The negative …
Why couldn't Rutherford's nuclear model explain the stability of the atom?
Answer
The Problem with Rutherford's Model: Classical electromagnetism states that any accelerating charged particle must radiate electromagnetic energy. In Rutherford's model: • Electrons revolve around n…
An electron in hydrogen atom jumps from n = 4 to n = 2. Calculate the frequency of the emitted photon. (R = 2.17 × 10⁻¹⁸ J, h = 6.626 × 10⁻³⁴ J·s)
Answer
Formula: νₘₙ = (R/h) × (1/m² − 1/n²) Given: • m = 2 (final orbit) • n = 4 (initial orbit) • R = 2.17 × 10⁻¹⁸ J • h = 6.626 × 10⁻³⁴ J·s Step 1: ν = (R/h) × (1/2² − 1/4²) Step 2: ν = (2.17 × 10⁻¹⁸ / 6…
What are the key observations of Rutherford's alpha particle scattering experiment?
Answer
Key Observations of Rutherford's Experiment: 1. Most α-particles passed straight through the gold foil — only small deflections. (Expected result — consistent with Thomson's model too) 2. A small fr…
Derive the expression for the speed of an electron in the nth orbit of hydrogen atom using Bohr's model.
Answer
Derivation: From Bohr's quantization condition: mvₙrₙ = nh/2π ...(1) From Bohr's first postulate (centripetal = Coulomb force): mvₙ²/rₙ = e²/(4πε₀rₙ²) → rₙ = e²/(4πε₀mvₙ²) ...(2) Substitute rₙ fr…
Calculate the wavelength of the first line of the Balmer series of hydrogen. (Rydberg constant = 1.097 × 10⁷ m⁻¹)
Answer
Balmer series: electron jumps to n = 2 from higher orbits. First line: n = 3 → n = 2 (Hα line) Formula: 1/λ = R(1/m² − 1/n²) Given: • R = 1.097 × 10⁷ m⁻¹ • m = 2, n = 3 Step 1: 1/λ = 1.097 × 10⁷ × …
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