Chapter 7, Problem 7.78P

Interpretation Introduction

Interpretation:

The total number of photons absorbed by the water in the soup to raise its temperature from $20°\text{C}$ to $98°\text{C}$ by absorption of radiation of wavelength $1.55\times {10}^{-2}\text{ m}$ is to be determined.

Concept introduction:

Electromagnetic waves are radiations that are formed by oscillating electric and magnetic fields. The electric and magnetic field components of an electromagnetic wave are perpendicular to each other.

Energy is proportional to the frequency and is expressed by the Plank-Einstein equation as follows:

$E=h\nu$

Here,

$E$ is the energy.

$h$ is the Plank’s constant.

$\nu$ is the frequency.

The equation to relate the frequency and wavelength of electromagnetic radiation is as follows:

$\nu =\frac{c}{\lambda }$

The equation to calculate the energy of a photon is,

$E=h\frac{c}{\lambda }$        (1)

Here,

$c$ is the speed of light.

$\lambda$ is the wavelength.

The specific heat capacity is defined as the amount of heat required to raise the temperature of $1\text{ g}$ of a substance by $1°\text{C}$.