The Abrupt Drop in Current in the Frank and Hertz Experiment: Explained

The Frank-Hertz experiment is a fundamental tool in the study of atomic energy levels and electron interactions. This phenomenon, observed through the behavior of current as a function of applied voltage, provides invaluable insights into the quantized nature of atomic systems. In this article, we will delve into the reasons behind the abrupt drop in current that occurs during the Frank-Hertz experiment.

Electron Acceleration and Energy Gain

Electrons in the Frank-Hertz experiment are accelerated through a potential difference, which imparts kinetic energy to them as they move towards the mercury vapor target. This acceleration is critical as it sets the stage for the subsequent energy transfer and atom excitation processes.

Energy Levels and Electron-Atom Interaction

Mercury atoms, like other elements, possess discrete energy levels. When an electron collides with a mercury atom, it can transfer its kinetic energy to the atom if the energy matches the difference between two quantized energy levels. This interaction is a key factor in understanding the abrupt drop in current.

Excitation of Mercury Atoms

At a specific voltage, approximately 4.9 eV for the first excitation level of mercury, the electrons have sufficient energy to excite the mercury atoms from their ground state to the first excited state. This transition is a critical phase in the experiment, where the electrons contribute to the current by exciting the mercury atoms, altering the dynamics of the system.

Energy Loss and Current Reduction

When an electron transfers energy to a mercury atom, it loses kinetic energy. This energy loss reduces the number of high-energy electrons available to contribute to the current, resulting in an abrupt drop in the current measured. This process repeats as the voltage is increased, with each excited state leading to a drop in current, followed by a recovery until the next energy level is reached.

Current Recovery and Repeated Experiments

As the voltage exceeds the energy required for the next excitation, the electrons can continue to gain energy and the current can increase again. This cycle creates a characteristic pattern of current versus voltage, showing peaks and drops corresponding to the excitation of the atoms. The pattern is a hallmark of the Frank-Hertz experiment and provides a clear demonstration of the energy levels in mercury atoms and the quantized nature of electronic transitions.

Understanding the Graph

The graph of current versus applied voltage clearly illustrates the linear increase in current as the voltage increases, until it encounters the quantum energy level of one of the mercury atom's shell electrons. At this point, the shell electron absorbs the quantum energy from the moving electrons, slowing them down and thus lowering the current. As the voltage increases further, the moving electrons gain more kinetic energy, reaching the next quantum energy level, leading to another drop in current.

The Frank-Hertz experiment provides a clear and tangible proof of the quantized nature of atomic energy levels. It is a cornerstone in the study of atomic and molecular physics, offering a practical method to observe and measure the discrete energy transitions in atoms.

By thoroughly understanding the mechanisms behind the abrupt drop in current, scientists can better comprehend the intricate interactions between electrons and atoms, further advancing our knowledge in atomic and subatomic physics.