Chapter 6, Problem 137AP

Interpretation Introduction

Interpretation:

The total number of photons required to elevate the temperature by 5.00°C is to be calculated.

Concept introduction:

The energy of n photons can be expressed as follows:

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

Here, $\text{E}$ denotes the energy of a 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:

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

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

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

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