How do you work out the wavelegth (Franck-Hertz experiment)?

In summary, in a Franck-Hertz experiment with potassium vapour, the current rapidly decreases at an applied voltage of 1.62V. Using the equation E=hc/lambda, the expected wavelength of the spectral line in the emission spectrum of potassium can be calculated as 3.08x10^-25. However, when checking with the value provided in a powerpoint, it should be 767nm, which can be obtained by using the correct value of 1.24 for the Planck constant and the speed of light in vacuum.
  • #1

Homework Statement

In a Franck-Hertz experiment carried out with potassium vapour, it is found that the current falls off rapidly at an applied voltage of 1.62V. Calculate the wavelength of the expected spectral line in the emission spectrum of potassium when this voltage is reached.

Homework Equations

E = hf = hc/lambda

The Attempt at a Solution

delta E = 1.62 eV
lambda = hc/1.62 = 3.08x10^-25

According to a powerpoint, it should be 1.24/eV = 1.24/1.62 = 767nm (which is right). Where does 1.24 come from?
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  • #2

1. What is the Franck-Hertz experiment?

The Franck-Hertz experiment is a classic physics experiment that demonstrates the quantization of energy in atoms. It involves passing an electric current through a gas at low pressure and measuring the voltage required to cause the gas atoms to emit light.

2. How does the Franck-Hertz experiment work?

The experiment involves a tube filled with a gas at low pressure, with a cathode at one end and an anode at the other. The cathode emits electrons, which accelerate towards the anode. However, some of the electrons collide with the gas atoms, transferring energy to them and causing them to emit light. The energy of the electrons can be controlled by varying the voltage between the cathode and anode, and the emitted light can be measured to determine the energy levels of the gas atoms.

3. What is the significance of the Franck-Hertz experiment?

The Franck-Hertz experiment provided evidence for the quantum nature of atoms, as it demonstrated that energy is quantized and that atoms have discrete energy levels. This experiment also helped to confirm the Bohr model of the atom and laid the foundation for further research in atomic physics.

4. How do you calculate the wavelength from the results of the Franck-Hertz experiment?

To calculate the wavelength, you need to know the voltage at which the gas atoms emit light. This can be determined by measuring the distance between the peaks in the current-voltage curve. The wavelength can then be calculated using the formula λ = hc/E, where h is Planck's constant, c is the speed of light, and E is the energy of the emitted light.

5. What are some limitations of the Franck-Hertz experiment?

One limitation of the Franck-Hertz experiment is that it only works for gases at low pressures. Additionally, it can only measure the energy levels of atoms that emit visible light, so it cannot be used for all elements. Finally, it is a relatively simple experiment and does not provide a complete understanding of the quantum behavior of atoms.

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