(a) Two sources generate light at wavelengths of λ=480 nm and λ=725 nm, respectively. What are

step 1 In this question we have to find the corresponding photon energies for each wavelength and also

(a) Two sources generate light at wavelengths of λ=480 nm...

(a) Two sources generate light at wavelengths of $\lambda=480 \mathrm{~nm}$ and $\lambda=725 \mathrm{~nm}$, respectively. What are the corresponding photon energies? ( $b$ ) Three sources generate light with photon energies of $E=0.87 \mathrm{eV}, E=1.32 \mathrm{eV}$, and $E=1.90 \mathrm{eV}$, respectively. What are the corresponding wavelengths?

Key Concepts

Wavelength-Energy Relationship

There is a fundamental inverse relationship between the wavelength of light and its energy, as described by the photon energy equation. This concept is pivotal in quantum mechanics because it shows that shorter wavelengths correspond to higher energies and longer wavelengths to lower energies, allowing the conversion between a photon’s energy and its wavelength.

Photon Energy

Photon energy refers to the quantized energy carried by a photon and is computed using the equation E = hc/?, where h is Planck’s constant and c is the speed of light. Understanding photon energy is essential for analyzing how light interacts with matter and for calculating the energy associated with specific wavelengths or frequencies of light.

Planck’s Constant and the Speed of Light

Planck’s constant (h) and the speed of light (c) are two fundamental physical constants that appear together in the equation for photon energy. They play a crucial role in connecting the energy and wavelength (or frequency) of electromagnetic radiation, thereby linking quantum mechanics with electromagnetic theory.

Unit Conversions (Joules and Electron Volts)

In many physics and chemistry problems, energy values need conversion between Joules and electron volts (eV). Mastering this conversion is important for ensuring that calculations are consistent and accurate, particularly when dealing with photon energies in various units.

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