The Emission of Radiation by Hydrogen Atoms in a Discharge Tube

What is the maximum and minimum wavelength of the radiation that can be emitted by hydrogen atoms when a beam of free electrons with an energy of 12.9 eV is fired at them?

Answer:

The maximum wavelength of radiation emitted by the hydrogen atoms can be calculated from the energy differences between various electron energy levels.

(a) The maximum wavelength of radiation emitted is 9.9 × 10^-8 meters.

(b) The minimum wavelength of radiation emitted is 19.0 × 10^-7 meters.

When a beam of free electrons with an energy of 12.9 eV is fired at hydrogen atoms in a discharge tube, the electrons can excite the hydrogen atoms to higher energy levels. As the electrons transition back to lower energy levels, they release energy in the form of radiation with specific wavelengths.

The maximum wavelength of the radiation emitted corresponds to the energy difference between the highest energy level the electron is excited to (n=4) and the ground state (n=1). This results in a maximum wavelength of 9.9 × 10^-8 meters.

On the other hand, the minimum wavelength of radiation emitted is determined by the energy difference between the first excited state (n=3) and the ground state (n=1). This results in a minimum wavelength of 19.0 × 10^-7 meters.

These calculations are based on the principles of quantum mechanics and the behavior of electrons in the hydrogen atom. The emission of radiation by hydrogen atoms provides valuable insights into the atomic structure and energy levels within the atom.