Chapter 9, Problem 9.89P

Interpretation Introduction

Interpretation:

The frequency, wavelength, and minimum energy of a photon that can free an H atom from water are to be calculated.

Concept introduction:

Energy is inversely proportional to the wavelength and directly proportional to the frequency and the expression to relate energy and frequency are as follows:

$E=\frac{hc}{\lambda }$ (1)

Or,

$E=hv$ (2)

Here,

$E$ is the energy of the photon.

$h$ is the Planck’s constant.

$c$ is the speed of light in vacuum.

$\lambda$ is the wavelength of the photon.

$v$ is the frequency of the photon.

The conversion factor to convert energy $\left(\text{J/mol}\right)$ into energy $\left(\text{J/photon}\right)$ is as follows:

$\text{Energy}\left(\text{J/photon}\right)=\text{Energy}\left(\text{J/mol}\right)\left(\frac{1\text{mol}}{6.022\times {10}^{23}\text{photons}}\right)$