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# Determining lowest excitation energy using the Franck-Hertz experiment

Abstract

Abstract

The lowest excitation energy of the elements Neon, Mercury, and Argon was determined by analyzing the fundamental properties of the signal structure in the Franck-Hertz experiment. In order to accurately determine the lowest excitation energy a new method proposed in (Rapior 2006) was employed. The main idea is that the spacings between the minima in the Franck Hertz curve increase linearly due to the additional acceleration over the mean free path. Therefore a linear fit was applied to graphs of spacings $$\Delta E$$ versus minimum order $$n$$. The fit estimated the lowest excitation energies of Neon ($$19.54\pm 1.48eV$$), Mercury ($$4.72\pm.25eV$$), and Argon ($$11.36\pm.38eV$$) accurately within experimental uncertainty.

## Introduction

The Franck-Hertz experiment demonstrates the quantum behavior of atoms and provides outstanding evidence that the transfer of energy to electrons should always be discrete, regardless of the mechanism of energy transfer. Furthermore it affirms the theory that all atoms consist of discrete stationary energy levels. Franck and Hertz focused their experiment on energy transfer by low-energy electron bombardment, so no other methods of energy transfer were included in the particular experiment. It was theorized that if the atoms being bombarded do not become ionized, then almost the entire energy of the bombarding electron will be transferred to the atomic system. In this version of the experiment only the energy required to excite the first energy levels were determined, although it is possible to find the excitation energy for levels of a higher order.

## Experiment

A typical arrangement of the Franck-Hertz experiment consists of an electron-emitting filament and a means of accelerating electrons to a variable potential. Accelerated electrons then bombarded atoms of the element, which are in a gaseous state. These accelerated electrons can either collide elastically or inelastically with atoms of the given element. Slowly moving electrons will collide elastically with atoms, which will change the path of the electron, but not its speed. Since the path of an electron that has undergone an elastic collision changes, the amount of time it takes the electron to reach the anode increases, but since its speed should not change the kinetic energy of the electrons should not change. When electrons have been accelerated to a potential that is equal to the discrete energy of the first excited level, collisions with atoms of the element become inelastic. The speed of the electron will decrease, which corresponds to a decrease in kinetic energy. Furthmore the collision should excite the atom. In order to detect the loss of kinetic energy, a small retarding potential exists before the anode, so that electrons that have lost most of their energy will not be able to overcome it, and thus will not reach the region of collection. This should correspond to a decrease in current of the electron beam. Thus in order to detect the excitation of atoms and the subsequent drop in kinetic energy, the current of the electron beam can be plotted.