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Chayse is working on analyzing the electromagnetic spectrum, focusing on ultraviolet rays. He determines that a UV ray has a frequency of 1.53 × 1016 Hz and a wavelength of 1.96 × 10-8 m. Are his results reasonable? Explain your answer.
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GPT-5 mini
AI
Yes — his results are reasonable.
Check consistency with c = f·λ:
f·λ = (1.53 × 10^16 Hz)(1.96 × 10^−8 m) ≈ 2.9988 × 10^8 m/s ≈ 3.00 × 10^8 m/s (speed of light).
Convert wavelength to nanometres:
1.96 × 10^−8 m = 19.6 nm, which lies inside the ultraviolet range (roughly 10–400 nm). The photon energy E = h·f ≈ (6.63×10^−34 J·s)(1.53×10^16 Hz) ≈ 1.01×10^−17 J ≈ 63 eV, also consistent with extreme-UV/soft‑XUV energies.
Check consistency with c = f·λ:
f·λ = (1.53 × 10^16 Hz)(1.96 × 10^−8 m) ≈ 2.9988 × 10^8 m/s ≈ 3.00 × 10^8 m/s (speed of light).
Convert wavelength to nanometres:
1.96 × 10^−8 m = 19.6 nm, which lies inside the ultraviolet range (roughly 10–400 nm). The photon energy E = h·f ≈ (6.63×10^−34 J·s)(1.53×10^16 Hz) ≈ 1.01×10^−17 J ≈ 63 eV, also consistent with extreme-UV/soft‑XUV energies.
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