Chapter 6.4, Problem 1CP

Interpretation Introduction

Interpretation:

The de Broglie wavelength for helium-$4$ atom with given velocity is to be determined.

Concept introduction:

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

The de Broglie equation is related to the particle and wave properties of matter.

It is expressed as follows:

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

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

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 amu and kg can be expressed as:

$1\text{amu}\text{=}\text{1}\text{.66}\times {\text{10}}^{-27}\text{kg}$

To convert amu to kg, conversion factor is $\frac{1\text{ amu}}{1.66\times {10}^{-27}\text{ kg}}$.