Which has higher energy, infrared radiation with λ=1.0 ×10^-6 m or an X ray with λ=3.0 ×10^-9

step 1 So the first part of this problem, we'll get in two wavelengths. So I'll write those out here. A

Which has higher energy, infrared radiation with λ=1.0...

Which has higher energy, infrared radiation with $\lambda=1.0 \times 10^{-6} \mathrm{~m}$ or an $\mathrm{X}$ ray with $\lambda=3.0 \times 10^{-9} \mathrm{~m} ?$ Radiation with $\nu=4.0 \times 10^{9} \mathrm{~Hz}$ or with $\lambda=$
$9.0 \times 10^{-6} \mathrm{~m} ?$

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Key Concepts

Electromagnetic Spectrum

The electromagnetic spectrum is the complete range of electromagnetic radiation, categorized by wavelength and frequency. It includes all types of radiation from long-wavelength, low-energy radio waves to short-wavelength, high-energy gamma rays. Understanding this spectrum is essential for determining the relative energies of different radiation types, such as infrared versus X-rays.

Photon Energy

Photon energy is defined by the relationship E = hf or equivalently E = hc/?, where E is the energy, f is the frequency, ? is the wavelength, h is Planck's constant, and c is the speed of light. This concept illustrates that a photon's energy is directly proportional to its frequency and inversely proportional to its wavelength.

Wavelength-Frequency Relationship

The inverse relationship between wavelength and frequency means that as the wavelength decreases, the frequency increases, leading to higher energy photons. This principle is critical when comparing different types of electromagnetic radiation, as shorter wavelengths correspond to higher photon energies.

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