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What is the wavelength (in nm) of the most intense radiation emitted from the surface of Mercury at high noon? (Hint: Use Wien's law, 2.90 x 106 m K Amax %3D T (in K) nm In which band of the electromagnetic spectrum is that wavelength? (Hint: Examine the following figure.) Visible light Short wavelengths Long wavelengths 4 x 107 (400 nm) 5 x 107 (500 nm) 6 x 107 (600 nm) 7 x 107 meters (700 nm) Wavelength (meters) 10-12 10-10 10-8 104 10-2 1 102 104 Ultra- Micro- Gamma- ray X-ray Infrared Radio violet wave UHF VHE FM AM Opaque Visual window Radio window Transparent b Short Wavelength Long Opacity of Earth's atmosphere

What is the wavelength (in nm) of the most intense radiation emitted from the surface of Mercury at high noon? (Hint: Use Wien's law, 2.90 x 106 m K Amax %3D T (in K) nm In which band of the electromagnetic spectrum is that wavelength? (Hint: Examine the following figure.) Visible light Short wavelengths Long wavelengths 4 x 107 (400 nm) 5 x 107 (500 nm) 6 x 107 (600 nm) 7 x 107 meters (700 nm) Wavelength (meters) 10-12 10-10 10-8 104 10-2 1 102 104 Ultra- Micro- Gamma- ray X-ray Infrared Radio violet wave UHF VHE FM AM Opaque Visual window Radio window Transparent b Short Wavelength Long Opacity of Earth's atmosphere

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## Understanding the Wavelength of Radiation from Mercury ### Calculating the Wavelength To determine the wavelength (in nanometers) of the most intense radiation emitted from the surface of Mercury at high noon, we use Wien's Law, expressed as: \[ \lambda_{\text{max}} = \frac{2.90 \times 10^6 \, \text{m} \cdot \text{K}}{T \, (\text{in K})} \] ### Electromagnetic Spectrum Analysis To identify the band of the electromagnetic spectrum corresponding to this wavelength, we examine the diagram below. ### Diagram Explanation #### Part A: Electromagnetic Spectrum Overview - The spectrum ranges from short to long wavelengths and includes: - Gamma-ray: \(10^{-12}\) meters - X-ray: \(10^{-10}\) meters - Ultraviolet: \(10^{-8}\) meters - Visible light: \(400 \, \text{nm} \) (violet) to \(700 \, \text{nm}\) (red) - Infrared - Microwave - Radio waves (UHF, VHF, FM, AM) #### Part B: Earth's Atmospheric Opacity - Illustrates the Earth's atmosphere's opacity across various wavelengths: - Opaque regions block certain wavelengths. - Transparent regions, like the "visual window" and "radio window," allow specific wavelengths to pass through the atmosphere. This visual guide helps correlate the calculated wavelength with its respective position in the electromagnetic spectrum, providing insights into atmospheric transparency at different wavelengths.
Transcribed Image Text:## Understanding the Wavelength of Radiation from Mercury ### Calculating the Wavelength To determine the wavelength (in nanometers) of the most intense radiation emitted from the surface of Mercury at high noon, we use Wien's Law, expressed as: \[ \lambda_{\text{max}} = \frac{2.90 \times 10^6 \, \text{m} \cdot \text{K}}{T \, (\text{in K})} \] ### Electromagnetic Spectrum Analysis To identify the band of the electromagnetic spectrum corresponding to this wavelength, we examine the diagram below. ### Diagram Explanation #### Part A: Electromagnetic Spectrum Overview - The spectrum ranges from short to long wavelengths and includes: - Gamma-ray: \(10^{-12}\) meters - X-ray: \(10^{-10}\) meters - Ultraviolet: \(10^{-8}\) meters - Visible light: \(400 \, \text{nm} \) (violet) to \(700 \, \text{nm}\) (red) - Infrared - Microwave - Radio waves (UHF, VHF, FM, AM) #### Part B: Earth's Atmospheric Opacity - Illustrates the Earth's atmosphere's opacity across various wavelengths: - Opaque regions block certain wavelengths. - Transparent regions, like the "visual window" and "radio window," allow specific wavelengths to pass through the atmosphere. This visual guide helps correlate the calculated wavelength with its respective position in the electromagnetic spectrum, providing insights into atmospheric transparency at different wavelengths.
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