Chapter 6.5, Problem 1PPB

Interpretation Introduction

Interpretation:

The momentum of a photon of radiation having wavelength $810\text{ nm}$ is to be determined.

Concept introduction:

The de Broglie equation is related to the particle and wave properties. It is expressed as follows:

$\lambda =\frac{\text{h}}{mu}$

Here, $\text{h}$ is Planck’s constant $\left(6.63\times {10}^{-34}\text{ J}\cdot \text{s}\right)$, $\lambda$ is the wavelength of moving particle, $m$ is its mass, and $u$ is its velocity.

Momentum is the product of mass and velocity of a moving particle. It is denoted by $p$.

The relationship between $\text{J}$ and $\text{kg}{\text{m}}^2{\text{s}}^{-2}$ can be expressed as:

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

To convert $\text{J}$ to $\text{kg}{\text{m}}^2{\text{s}}^{-2}$, conversion factor is $\frac{{\text{1 kg m}}^2{\text{ s}}^{-2}}{1\text{ J}}$.

The relationship between meters $\text{(m)}$ and nanometres $\text{(nm)}$ can be expressed as:

$\text{1nm = 1}\times {\text{10}}^{-9}\text{m}$

To convert meters $\text{(m)}$ to nanometres $\text{(nm)}$, conversion factor is $\frac{1\text{ nm}}{1.00\times {10}^{-9}\text{ m}}$.