Chapter 27, Problem 51A

a.

To determine

To Describe: A method to measure charge of an electron.

Explanation of Solution

Introduction:

Charge of an electron is $-1.6021\times {10}^{-19}\text{C}$ . It was determined by Millikan’s oil drop experiment.

In the experiment, Millikan suspended a small oil drop which was charged within the presence of electric field. By equating the weight of the oil drop with electrostatic force on it, the amount of charge on an electron was determined.

b.

To determine

To Describe: A method to measure mass of an electron.

Explanation of Solution

Introduction:

Mass of electron is $9.1\times {10}^{-31}\text{kg}$ . The charge of the electron was determined using Millikan’s oil drop experiment. The mass of the electron was then determined using the known charge to mass ratio.

The value of charge to mass ratio was determined by JJ Thomson.

  $\frac{e}{m}=-1.758\times {10}^{11}\text{C/kg}$

The charge of an electron is $-1.6021\times {10}^{-19}\text{C}$ .

The mass of the electron was then calculated as follows:

  $\begin{array}{l}m=\frac{e}{-1.758\times {10}^{11}\text{C/kg}}=\frac{-1.6021\times {10}^{-19}\text{C}}{-1.758\times {10}^{11}\text{C/kg}}\\ m=9.1\times {10}^{-31}\text{kg}\end{array}$

c.

To determine

To Describe: A method to measure wavelength of an electron.

Explanation of Solution

Introduction:

Mass of electron is $9.1\times {10}^{-31}\text{kg}$ .

As per de Broglie’s equation, $\lambda =\frac{h}{p}$

Here, h is the Planck’s constant, p is the momentum and $\lambda$ is the wavelength.

Using the de Broglie’s wavelength equation and with the knowledge of the speed of the electron, the wavelength of the electron can be measured.