What is the energy of each of the following photons in kilo...

What is the energy of each of the following photons in kilo joules per mole?

(a) $\nu=5.97 \times 10^{19} \mathrm{s}^{-1} \quad$ (b) $\nu=1.26 \times 10^{6} \mathrm{s}^{-1}$
(c) $\lambda=2.57 \times 10^{2} \mathrm{m}$

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Key Concepts

Unit Conversion

Unit conversion involves converting the energy from joules, the standard unit of energy for a single photon, to kilojoules per mole. This process requires multiplying the energy per photon by Avogadro's number and then converting joules to kilojoules, ensuring consistency in scientific calculations and communication.

Avogadro's Constant

Avogadro's constant represents the number of particles, such as atoms or photons, in one mole of a substance. It plays a crucial role in converting the energy calculated for a single photon into the energy per mole, which is useful for comparing and measuring energy on a macroscopic scale.

Frequency and Wavelength Relationship

The relationship between frequency and wavelength is given by the equation c = ??, where c is the speed of light, ? is the wavelength, and ? is the frequency. This concept is essential when converting between wavelength and frequency so that photon energy can be computed using Planck's equation.

Planck's Equation

Planck's equation, E = h?, relates the energy (E) of a photon to its frequency (?) using Planck's constant (h). This is a fundamental concept in quantum mechanics that shows energy is quantized, and it provides the basis for calculating the energy of electromagnetic radiation at the atomic and molecular levels.

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