Physics

Problem

Engineers are designing a layered radiation shield for a lunar habitat. They must account for the full range of electromagnetic radiation likely to be encountered. The following list compiles representative radiation that could strike the shield. Each entry includes either a wavelength, a frequency, or a photon energy. 1. Long-range radio transmission:

\lambda=1.0\,\text{km}

2. Microwave downlink: 12 GHz 3. Thermal infrared emission:

\lambda=8\,\text{µm}

4. Visible blue light:

\lambda=450\,\text{nm}

5. Ultraviolet from the Sun:

\lambda=200\,\text{nm}

6. Medical X-ray spill: photon energy

E=5\,\text{keV}

7. Cosmic gamma rays:

f=3.0\times10^{20}\,\text{Hz}

8. Seismic surface wave generated by a nearby impact (distractor) Constants:

c=3.0\times10^{8}\,\text{m\,s}^{-1}

h=6.63\times10^{-34}\,\text{J\,s}

1\,\text{eV}=1.6\times10^{-19}\,\text{J}

. (a) For each listed electromagnetic entry (exclude the seismic wave), compute its frequency in hertz. Show the conversion steps for every item, explicitly indicating how wavelengths and photon energies were translated into frequency. (b) Using the numerical frequencies obtained in part (a), produce a complete ranking of the electromagnetic entries from lowest to highest frequency. Present the final ordered list by item number and description. (c) Provide a concise but logically ordered justification for your ranking, citing specific numerical evidence and the fundamental relationships among wavelength, frequency, and photon energy. (d) Focusing on items 3, 4, and 5, explain why the visible blue light is situated between the infrared and ultraviolet regions in your ranking. In your explanation, connect your numerical work to conventional definitions of these spectral regions.

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