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If you have difficulty with only one or two of the questions you should follow the guidance given in the answers and read the relevant parts of the module.
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If you are sure that you can meet each of these achievements, try the Subsection 4.3Exit test. Study comment Can you answer the following Fast track questions? If you answer the questions successfully you need only glance through the module before looking at the Subsection 4.1Module summary and the Subsection 4.2Achievements. If not, proceed directly to the Subsection 1.3Ready to study? Subsection. If so, try the following Fast track questions. Study comment Having read the introduction you may feel that you are already familiar with the material covered by this module and that you do not need to study it. Finally a comparison between the Schrödinger model and the Bohr model is made. Section 3 introduces the Schrödinger model, setting up the Schrödinger equation for atomic hydrogen, describing its solutions and the quantum numbers which arise from these solutions. In Section 2 we review the Bohr model for hydrogen and the early ideas of de Broglie waves as applied to the Bohr model. This non–classical wave behaviour completely undermines the Bohr approach – the electron may not be considered classically at all, not even ‘semi-classically’. This idea was incorporated in to the ‘new quantum theory’ which is expressed by the Schrödinger wave equation. This had been suggested by Louis de Broglie and was confirmed by the observation of electron diffraction. The situation was changed again when it was discovered that the electron had wave–like properties. Attempts to extend the simple circular orbit model and to introduce refinements required by Einstein’s theory of relativity led to inconsistencies between predictions and experimental observations.
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However, as frequently happens, the success did not survive closer examination and the advances in knowledge after Bohr’s work. It used an amalgam of classical physics and what has become known as the ‘old quantum theory’. This theory represented a significant advance on classical physics. We will look at the elements of Bohr’s argument in Subsection 2.1. Transitions by the electron between these levels, according to Bohr’s quantum theory of the atom, correctly predicted the wavelengths of the spectral lines. He started by looking at the electron in a circular orbit about the proton and derived an expression for the corresponding energy levels. Application to the hydrogen atom was first tried by Niels Bohr in 1913. Radiation of frequency f transfers its energy in quanta of amount hf. Initially, the theory was applied to radiation. The arrival of the quantum theory at the beginning of the twentieth century offered a new approach.
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Classical theory, therefore, not only fails to predict the characteristic line spectra, it suggests that the atom is inherently unstable! The loss of energy by the electron will cause it to spiral in towards the proton and eventually crash into it within a tiny fraction of a second. Indeed, the theory predicts that an electron in orbit about the proton will continuously emit electromagnetic radiation. However, even after the discovery of the nuclear atom by Rutherford in 1912, the classical physics of the nineteenth century, when applied to the electron in the atom, could not account for the hydrogen spectrum at all. This was before the discovery of the electron, so no theory could be put forward to explain the simple formulae. Nineteenth century physicists, starting with Balmer, had found simple formulae that gave the wavelengths of the observed spectral lines from hydrogen. In this module, we will look at the attempts that have been made to understand the structure of the hydrogen atom – a structure that leads to a typical line spectrum. It is therefore not surprising that it has been the test–bed for new theories. It has only one electron and the nucleus is a proton.