In 1914, a pivotal result was obtained after the Franck-Hertz experiment that made even Albert Einstein say, "It's so lovely it makes you cry." James Franck and Gustav Hertz had multiple questions: Are there gaps between the amounts of energy an atom can have? Could the atom hit by the electron take some energy and store it as an internal energy gain? If it can store, can this energy take any value from small to large? Or is it selected in values that are strictly limited to certain amounts? To seek answers to their questions, James Franck and Gustav Hertz experimented with bombarding atoms with electrons. This article will help you understand the experiment and its applications.
Explanation of Franck Hertz's experiment
The Franck-Hertz experiment is a historically significant physics experiment. The Bohr-atom model, which pioneered quantum mechanics, was firmly supported by this experiment. Moreover, it is the first experimental verification of the existence of discrete energy states in atoms, performed (1914) by the German physicists James Franck and Gustav Ludwig Hertz.
Aim
The purpose of the experiment is to demonstrate the concept of quantization of the energy levels under Bohr's model of an atom.
Materials required
- Power supply
- A control unit for the power supply
- A DC amplifier
- Oven
- Mercury filled tube
- Neon filled tube
Theory
Originally, the experiment was carried out with the help of a vacuum tube at a temperature of \(115 °C.\) The tube was placed with the help of three electrodes - a cathode which emits electrons, a metal grid and an anode. The voltage of the grid is kept positive with respect to the cathode to draw more electrons towards it.
Since the grid is kept at a positive potential, electrons are accelerated towards it after they are emitted by the cathode. The collecting plate is kept at a negative potential with respect to the grid. Reaching the grid, some will pass through it, and some will be slowed down and fall back into the grid. Those will reach the plate, and the equivalent current will be measured.
As long as the collision is elastic, there is no loss of energy. The current increases as the voltage increase till it reaches a particular value - \(4.9\;\mathrm{eV}\) for Mercury and \(19\;\mathrm{eV}\) for neon, where the collision becomes inelastic. The electron loses its energy and the measured current drops.
Conclusion
This resulted in the prediction of quantum theory that electrons occupy only discrete, quantized energy states.
The heated vacuum tube being used in the Frank-Hertz experiment has three electrodes here. Inside the tube, there are droplets of mercury, which are not visible in the picture though. C is the cathode that emits electrons, which pass through the mesh grid G, and are ultimately collected as electric current by the anode, Wikimedia Commons
Applications of the Franck-Hertz experiment
In this section, we will learn more about the two types of collisions, elastic and inelastic, early quantum theory, and the Frank-Hertz experiment with neon gas.
Modeling of Electron Collisions with Atoms
Franck and Hertz explained the experiment in terms of collisions between the electrons and the mercury atoms. When the speed of elastic collision of electrons exceeds about 1.3 million meters per second, it becomes inelastic. This speed is equivalent to the kinetic energy of \(4.9\;\mathrm{eV}\). When the voltage reaches \(4.9\;\mathrm{eV}\), it results in the slowing down of electrons, resulting in a drop in current.
Elastic collision
If the electron does not have enough energy to raise the atom to a higher energy level, the collision of the electron sent onto the atom will be elastic. The electron leaves the gas chamber without losing its energy.
Inelastic collision
If the energy of the electron is higher than the excitation energies of the atom, the atom receives the energy required for its excitation from the electron, and if there is, the electron leaves the gas chamber with its remaining energy. This collision is called an inelastic collision.
Representation of Elastic vs Inelastic collisions of electrons. After elastic collisions, electrons traveling slowly change their direction, but the speed remains as it is. In an inelastic collision, electrons travel much faster, losing their speed. The lost kinetic energy is thereby deposited into mercury Hg atoms, consequently emitting light and returning to their original state, Wikimedia commons
Early quantum theory
The basic principle of the Bohr model is that the possible binding energies of an electron to the nucleus of an atom are discrete. A positive ion will be produced as the collision happens at the binding energy, ejecting the electron from the atom.
The Bohr model of the atom, although not a completely up-to-date quantum model of the atom, describes many of the accepted features of atomic theory.
The Bohr model describes the atom as consisting of negatively charged electrons orbiting in circles, due to the Coulomb force, around a central positively charged nucleus. In Bohr's model, the electrons can only orbit at certain radii, and the electron's energy remains constant at each radius. The electron can move from one energy level to another by absorbing or emitting radiation. The Franck-Hertz experiment provided support for the Bohr model of the atom. In the Franck-Hertz experiment, electrons were accelerated through a low-pressure gas.
Hence, the Franck-Hertz experiment is the first direct experimental proof of the Bohr relation.
Experiment with neon
For Neon gas, when the accelerated voltage excites the electrons in the gas, it produces a glow. There are about ten exciting levels within the range of \(18.3\;\mathrm{eV}\) to \(19.5\;\mathrm{eV}\). The energy difference between excited and de excited levels gives the light in the visible range of the spectrum. Likewise, the scenario is observed in neon gas at about \(19\;\mathrm{eV}\). An additional advantage of neon for instructional laboratories is that the tube can be used at room temperature.
Electronvolt \(\mathrm{eV}\), which is a very small energy unit, is used to indicate the energies of electrons.
Graph of Frank Hertz's experiment
The graph of the Frank-Hertz experiment showing the behaviour of current with different voltages. The rise in the curve corresponds to the region where electrons gain kinetic energy due to excitation potential but not enough to ionize mercury. The decaying in the curve indicates medium is ionized energy is lost in ionization. The distance between two maxima is constant and equals the excitation potential of the medium. However, mercury has more than one excitation and ionization potential which makes the second and third peaks of the curve complicated. The discrete number of humps suggest that the electrons give energy to the atoms in only discrete levels. Wikimedia Commons
Observations from the graph:
- The current through the tube increased gradually with an increasing potential difference at low potential differences up to \(4.9\;\mathrm{V}\). Increased voltages result in a larger space-charge limited current, which is typical of real vacuum tubes that do not contain mercury vapor.
- The current decreases dramatically at \(4.9\;\mathrm{V}\), practically to nothing.
- As the voltage is increased higher, the current increases gradually until it reaches \(9.8\;\mathrm{V}\).
- A similar dramatic decline may be seen at \(9.8\;\mathrm{V}\)
- This series of decreases in current at around\(4.9\;\mathrm{V}\) increments continues until potentials of at least \(70\;\mathrm{V}\), even though it isn't visible in the original measurements of the figure.
Formula of Frank-Hertz experiment
Atoms in excited states emit radiation at discrete frequencies. The frequency of the radiation \(\nu\) is mathematically represented as :
\[\Delta E = h\nu\]
where \(\Delta E\) is the change in the atomic energy levels and \(h\) is the Planck constant.
With the emission of radiation at discrete frequencies, it is direct evidence that energy levels are quantized.
Proof of the experiment
This figure shows the energy levels that electrons can occupy in a mercury atom. The ground state and ionization energy can also be seen. StudySmarter Originals
If an electron with an energy of \(4.9\;\mathrm{eV}\) collides with a mercury atom, this gas atom gains energy and becomes unstable. After a short time, it scatters this energy as photons and returns to its ground state. The electron continues on its way with an energy of \(0.04\;\mathrm{eV}\)
An electron with an energy of \(3.85\;\mathrm{eV}\) does not change the energy of the mercury atom. In other words, this electron passes through the atom without excitation.
The largest value of the energy levels is called the ionization energy (\(10.40\;\mathrm{eV}\) for Mercury). If the energy of the electron is greater than or equal to the ionization energy, the atom is ionized. If the mercury atom is excited with an electron with an energy of \(12.00\;\mathrm{eV}\), an electron is removed from the atom and becomes a positively charged ion.
The state in which the atom is before any excitation energy is given is called the ground state. The smallest energy value that can remove an electron from an atom is called ionization energy.
Frank-Hertz Experiment - Key takeaways
- The Bohr-atom model, which pioneered quantum mechanics, was confirmed by the Franck-Hertz experiment.
- It has been verified by the Franck-Hertz experiment that atoms can absorb energy not in the form of more or less but in discontinuous amounts.
- Electrons coming out of the electron gun lose a certain amount of energy when they collide with the gas atoms in the mercury gas section. Gas atoms in the ground state become unstable. The ground state is the most stable state of the atom.
- Electronvolt \(\mathrm{eV}\) , which is a very small energy unit, is used to indicate the energies of electrons and is equal to the energy gained by an electron on moving through a potential difference of \(1\;\mathrm{V}\)
- The state in which the atom is before any excitation energy is given is called the ground state.
- The smallest energy value that can remove an electron from an atom is called ionization energy.
References
- Albert Einstein, "It's so lovely it makes you cry." APS Physics, April 2017
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