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#electron velocity

14 public questions tagged with this topic.

De Broglie Wavelength and Matter Waves

The de Broglie wavelength of an electron is \( 0.2 \, \text{nm} \). What is its speed? (Take \( h = 6.63 \times 10^{-34}

**Matter waves** wave-like properties of moving particles, macroscopic objects not exhibit measurable wave-like because λ = h/(m v) extremely small for large m, e.g., 1 kg at 1 m/s λ=6.6×10⁻³⁴ m undetectable, for electron 9.11×10⁻³¹ kg at 2×10⁶ m/s λ=0.36 nm measurable via diffraction, de Broglie hypothesis λ = h/p proposed by de Broglie 1924, Davisson-Germer experiment confirmed. p = (h/λ) = (6.63 × 10⁻³⁴/0.2 × 10⁻⁹) = 3.315 × 10⁻²⁴ kg m/s . v = (p/m) = (3.315 × 10⁻²⁴/9.11 × 10⁻³¹) ≈ 3.64 × 10⁶ m/s . Applying E = h f = h c/λ, p = h/λ, K_max = h f -

Ref: NCERT > Physics Book > Dual Nature of Matter > De Broglie Wavelength and Matter Waves

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Bohr Model Energy Levels and Hydrogen Spectrum

What is the speed of an electron in the \( n = 4 \) orbit of a hydrogen atom if its speed in \( n = 1 \) is \( 2.2 \time

**Bohr energy levels** E_n = -13.6/n² eV for hydrogen, negative indicating bound state, total energy = -13.6 eV ground state n=1, -3.4 eV n=2, -1.51 eV n=3, etc., photon energy for transition n_i → n_f is ΔE =13.6(1/n_f² -1/n_i²) eV, wavelength λ = hc/ΔE, h=6.6×10⁻³⁴ J·s, c=3×10⁸ m/s. Emission line spectrum characterized by discrete wavelengths because energy levels discrete. v_n = (v₁/n) . For n = 4 : v₄ = (2.2 × 10⁶/4) = 5.5 × 10⁵ m/s . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5

Ref: NCERT > Physics Book > Atoms and Nuclei > Bohr Model Energy Levels and Hydrogen Spectrum

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Temperature Dependence of Resistance and Resistivity

A copper wire of cross-sectional area \( 2.5 \times 10^{-7} \, \text{m}^2 \) carries a current of \( 0.85 \, \text{A} \)

**Resistivity temperature variation** ρ_t = ρ₀[1+α(T-T₀)], α ≈4×10⁻³ /°C for copper, 1.7×10⁻⁴ /°C for nichrome. Given R=60 Ω at 30°C, α=1.7×10⁻⁴ /°C, T=330°C, ΔT=300°C, R_t=60[1+1.7×10⁻⁴×300]=60×1.051=63.06 Ω, modest increase for nichrome due to small α. Drift speed: v_d = (I/n e A) . Substitute: v_d = (0.85/8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 2.5 × 10⁻⁷) . Calculate: v_d = (0.85/3.4 × 10³) ≈ 2.5 × 10⁻⁴ m/s . Applying I = n e A v_d, R = ρ l/A, R_t = R₀[1+αΔT], Kirchhoff's ΣI=0, ΣV=0, R_eq series/parallel, V = ε - I r and P = I²R, evaluation yields 2.5 × 10⁻⁴ m/s, consistent

Ref: NCERT > Physics Book > Current Electricity > Temperature Dependence of Resistance and Resistivity

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