SOLUTION: Energy frequency wavelength worksheet quiz - Studypool - Free Printable

- Use the formula E = hν, where h = 6.626 × 10⁻³⁴ J·s and ν = 2.68 × 10⁶ Hz. Calculate E = (6.626 × 10⁻³⁴) × (2.68 × 10⁶) = 1.78 × 10⁻²⁷ J.
- For energy: E = hν = (6.626 × 10⁻³⁴) × (6.165 × 10¹⁴) = 4.08 × 10⁻¹⁹ J ≈ 4.1 × 10⁻¹⁹ J. For wavelength: λ = c/ν = (3.00 × 10⁸ m/s) / (6.165 × 10¹⁴ Hz) = 4.87 × 10⁻⁷ m.
- Convert wavelength to meters: λ = 400 nm = 400 × 10⁻⁹ m = 4.00 × 10⁻⁷ m. Frequency: ν = c/λ = (3.00 × 10⁸) / (4.00 × 10⁻⁷) = 7.50 × 10¹⁴ Hz. Energy: E = hν = (6.626 × 10⁻³⁴) × (7.50 × 10¹⁴) = 4.97 × 10⁻¹⁹ J.
- Wavelength: λ = c/ν = (3.00 × 10⁸) / (1.5 × 10¹⁷) = 2.0 × 10⁻⁹ m. Energy: E = hν = (6.626 × 10⁻³⁴) × (1.5 × 10¹⁷) = 9.94 × 10⁻¹⁷ J ≈ 9.95 × 10⁻¹⁷ J.
- Convert wavelength to meters: λ = 0.050 cm = 0.00050 m = 5.0 × 10⁻⁴ m. Energy: E = hc/λ = (6.626 × 10⁻³⁴ × 3.00 × 10⁸) / (5.0 × 10⁻⁴) = 3.98 × 10⁻²² J.
- Convert wavelength to meters: λ = 10.0 μm = 10.0 × 10⁻⁶ m = 1.00 × 10⁻⁵ m. Energy per photon: E_photon = hc/λ = (6.626 × 10⁻³⁴ × 3.00 × 10⁸) / (1.00 × 10⁻⁵) = 1.988 × 10⁻²⁰ J. Total energy required: 1.0 kJ = 1000 J. Number of photons = total energy / energy per photon = 1000 / (1.988 × 10⁻²⁰) = 5.03 × 10²² ≈ 5.0 × 10²² photons.
- Energy per photon: E_photon = hc/λ = (6.626 × 10⁻³⁴ × 3.00 × 10⁸) / (3.0 × 10⁻¹²) = 6.626 × 10⁻¹⁴ J. Total energy = number of photons × energy per photon = (1.5 × 10¹³) × (6.626 × 10⁻¹⁴) = 0.9939 J ≈ 1.0 J.
- Convert wavelength to meters: λ = 6.80 × 10⁻⁵ cm = 6.80 × 10⁻⁷ m. Frequency: ν = c/λ = (3.00 × 10⁸) / (6.80 × 10⁻⁷) = 4.41 × 10¹⁴ Hz ≈ 4.4 × 10¹⁴ Hz. Energy: E = hν = (6.626 × 10⁻³⁴) × (4.41 × 10¹⁴) = 2.92 × 10⁻¹⁹ J.
- Convert wavelength to meters: λ = 5.20 × 10⁻⁵ cm = 5.20 × 10⁻⁷ m. Frequency: ν = c/λ = (3.00 × 10⁸) / (5.20 × 10⁻⁷) = 5.77 × 10¹⁴ Hz.
- Convert wavelength to meters: λ = 4.25 × 10⁻⁷ m. Frequency: ν = c/λ = (3.00 × 10⁸) / (4.25 × 10⁻⁷) = 7.06 × 10¹⁴ Hz ≈ 7.1 × 10¹⁴ Hz. This frequency corresponds to UV radiation.