Chapter 9, Problem 9.77P

(a)

Interpretation Introduction

Interpretation:

The longest wavelength (in $\text{nm}$) that can dissociate a molecule of $\text{HI}$ is to be determined.

Concept introduction:

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

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

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.

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

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

(b)

Interpretation Introduction

Interpretation:

The excess energy over a photon of $\text{254}\text{nm}$ that is needed for dissociation is to be determined.

Concept introduction:

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

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

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.

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

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

(c)

Interpretation Introduction

Interpretation:

The speed when excess energy is carried away by the $\text{H}$ atom as kinetic energy is to be calculated.

Concept introduction:

The kinetic energy is the energy that arises due to the motion of the body. The formula to calculate kinetic energy is as follows:

$E=\frac{1}{2}m{u}^2$ (4)

Here,

$E$ is the kinectic energy of the body.

$m$ is the mass of the body.

$u$ is the speed of the body.

The conversion factor to convert $\text{J}$ into $\frac{\text{kg}\cdot {\text{m}}^2}{{\text{s}}^2}$ is as follows:

$\text{1}\text{J}=1\text{kg}\cdot {\text{m}}^2{\text{/s}}^2$