Chapter 6, Problem 135AP

Interpretation Introduction

Interpretation:

The number of photons is to be calculated when $92.0\%$ of microwave energy has been changed to thermal energy of water.

Concept introduction:

The energy of n photon can be expressed as follows:

$\text{E}=n\frac{\text{hc}}{\lambda }$

Here, $\text{E}$ denotes the energy of photon, $\text{h}$ denotes Planck’s constant $\left(6.63\times {10}^{-34}\text{ J}\cdot \text{s}\right)$, $\text{c}$ denotes the speed of light $\left(3.0\times {10}^8\text{ m/s}\right)$, and $\lambda$ denotes the wavelength.

The expression for specific heat capacity is as follows:

$\begin{array}{c}q=ms\Delta T\\ \text{or, }q=ms\left(T_f-T_i\right)\end{array}$

Here, $q$ denotes the energy, m denotes mass, $s$ denotes specific heat, and $\Delta T$ is the change in temperature from initial temperature $\left(T_i\right)$ to final temperature. $\left(T_f\right)$

The value of $s$ for water is $4.184\text{ J/g}\cdot °\text{C}$.

Conversion of meter to nanometer is $\frac{1.00\text{ nm}}{1.00\times {10}^{-9}\text{ m}}$.