Lab Report: Franck-Hertz Experiment

Section 1 – Introduction

The primary objective of this experiment is to observe the excited states of the mercury atom and investigate the energy transitions that occur during elastic and inelastic collisions between electrons and mercury atoms. The fundamental outcome of this experiment is the verification of the existence of discrete energy levels in the atomic structure.

According to Bohr's atomic model, electrons require ionization energy to transition to higher energy levels. In other words, energy is needed to remove electrons from an atom.

Bohr's theory suggests that the entire energy of an electron is quantized, and electrons do not lose energy during elastic collisions within the tube. The acceleration potential and current are directly proportional. The maximum acceleration potential for mercury atoms is 4.9 eV, which means that as electrons pass from one atom to another, their energy increases. The contact potential difference exists between the cathode and anode and represents the energy required to remove electrons from the cathode. In this experiment, the ionization process of mercury atoms within the tube is facilitated through a heating process.

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The minimum energy required to excite a mercury atom is 4.9 eV. Once the acceleration voltage reaches this value, the current begins to decrease. This occurs because an electron attempts to excite another electron with its energy, leading to energy loss and a subsequent decrease in current.

Section 2 – Experimental Details

The experimental setup consists of an oscilloscope, an oven, a thermometer, and the Franck-Hertz (FH) main unit. The oscilloscope is used to receive a signal and display the current-voltage graph.

The thermometer is employed for temperature measurements, while the FH main unit comprises the FH tube and a heater. Inside the FH tube, there are cathode, anode, and collector elements, along with mercury atoms. The heater is responsible for heating the cathode.

During the experiment, a filament voltage is applied to accelerate electrons towards the grid, where they are emitted from the heated cathode. The acceleration potential is generated by the movement of electrons between the cathode and the anode. The collector voltage is used to prevent electrons with low kinetic energy from forming sharp peaks between the anode and the collector.

Electrons emitted from the heated cathode move towards the grid and utilize an acceleration potential. Subsequently, these electrons pass through the grid and reach the collector due to a small voltage difference. The collector voltage plays a crucial role in determining the collector current, which is the measured parameter in this experiment. Different collectors are used to measure the current at various stages of the experiment. The resulting data is represented as collector current versus accelerated potential.

Section 3 – Measurement & Data Analysis

Data Set 1:

• Filament voltage = 6V
• Collector voltage = 2V
• Temperature = 180-150°C

Data Set 2:

• Filament voltage = 5V
• Collector voltage = 1V
• Temperature = 176-197°C

Voltage at first min/max [V]

Voltage at second min/max [V]

Voltage at third min/max [V]

Voltage differences between the first and the second min/max [V]

Voltage differences between the second and the third min/max [V]

Mean of Voltage Difference between min/max [V]

The excited energy level of Mercury

Table 1. Data for different filament and collector voltages.

From the accelerated voltage graph, it is observed that the period value for the first part is 5 V, while the period value for the second part is approximately 4.73 V. These values closely align with the theoretical expectations. It is worth noting that the work function of the anode is greater than that of the cathode. Furthermore, electrons with an acceleration voltage of 4.9 eV are accelerated once more, allowing for the observation of additional collisions. These collisions occur in multiples of 4.9 eV, as this value corresponds to the emission spectrum of mercury.

Section 4 – Calculations

For Part 1:

_{1. Calculation of Voltage Difference between the first and the second min/max [V]:}

^{Voltage Difference = Voltage at second min/max - Voltage at first min/max}

_{- For Data Set 1:}

^{Voltage Difference = 12.5 V - 8.5 V = 4 V}

_{- For Data Set 2:}

^{Voltage Difference = 13.0 V - 8.5 V = 4.5 V}

_{2. Calculation of Voltage Difference between the second and the third min/max [V]:}

^{Voltage Difference = Voltage at third min/max - Voltage at second min/max}

_{- For Data Set 1:}

^{Voltage Difference = 18.5 V - 12.5 V = 6 V}

_{- For Data Set 2:}

^{Voltage Difference = 18.0 V - 13.0 V = 5 V}

_{3. Calculation of the Mean Voltage Difference between min/max [V]:}

^{Mean Voltage Difference = (Voltage Difference between the first and the second min/max + Voltage Difference between the second and the third min/max) / 2}

_{- For Data Set 1:}

^{Mean Voltage Difference = (4 V + 6 V) / 2 = 5 V}

_{- For Data Set 2:}

^{Mean Voltage Difference = (4.5 V + 5 V) / 2 = 4.75 V}

Section 5 – Results and Discussion

The primary objective of this experiment was to experimentally validate Bohr's postulate regarding discrete energy levels in atoms. Based on the results obtained, it can be concluded that discrete energy levels were indeed observed in the course of this experiment.

One significant observation from the experiment was that when the acceleration voltage reached 4.9 eV, there was a noticeable decrease in the current value. This phenomenon indicates the occurrence of inelastic collisions, where electrons lose energy. Conversely, in elastic collisions, electrons do not lose much energy. When the voltage is increased beyond this threshold, electrons regain their energy and continue to excite the mercury atoms, resulting in a renewed flow of current. It is important to note that current and voltage exhibit a direct proportional relationship. As the current increases, so does the voltage, up to a certain point.

The presence of multiple peaks in the graph can be attributed to the occurrence of inelastic collisions, where electrons lose energy, leading to current drops, followed by the regaining of energy and subsequent current increases. The number of peaks in the graph is indicative of the extent of inelastic collisions.

In the graph generated from the data, it is observed that the voltage difference between the peaks is consistent. Theoretically, this corresponds to the inter-peak voltage contact voltage. The error value calculated from the data is 2.04% for the first part, which is a relatively low and acceptable error value considering the experimental environment's sensitivity to factors such as temperature. Similarly, the error value for the second part is 3.06%, which is also within an acceptable range. Additionally, the calculated excitation energy closely matches the theoretical value, indicating a successful achievement of the experiment's objectives.

It is important to note that high excitation energy levels were not observed in this experiment. This may be attributed to the difficulty in either achieving such high levels of energy or the challenge of stimulating atoms to regain lost energy at higher energy levels. It is established that each atom possesses a minimum energy requirement for excitation.

Section 6 – References

1. Krane, K. S. (2019). Modern physics. John Wiley & Sons.
2. Hanne, G. F. (1988). What really happens in the Franck–Hertz experiment with mercury? American Journal of Physics, 56(8), 696-700.
3. Serway, R. A., Moses, C. J., & Moyer, C. A. (2004). Modern physics. Cengage Learning.