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TheBohrQuantumModel - THE BOHR QUANTUM MODEL INTRODUCTION...

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1 THE BOHR QUANTUM MODEL INTRODUCTION When light from a low-pressure gas is subject to an electric discharge, a discrete line spectrum is emitted. When light from such a low-pressure gas is examined with a spectroscope, it is found to consist of a few bright lines of pure color on a dark background. The wavelength contained in a given line spectrum are characteristic of the particular element emitting the light. Because no two elements emit the same line spectrum, this phenomenon represents a practical and sensitive technique for identifying elements present in unknown samples. In 1885, by trial and error, Johann Balmer found a formula that predicted the wavelength for the four visible lines in the emission spectrum of hydrogen. The most general form of the formula is given by = 2 2 2 1 1 1 i f n n RZ λ (1) where n i and n f are integers, Z is the atomic number (Z=1 for hydrogen), and R is a constant called the Rydberg constant. These four lines of hydrogen are now known as the Balmer series. In 1913, Danish physicist, Niels Bohr proposed a revolutionary quantum model that impacted the scientific community. One of the triumphs of the Bohr Quantum Model was its remarkably successful agreement with the formula proposed by Balmer. The objective of this lab is: 1. To determine the Rydberg constant by analyzing the Balmer series of hydrogen. 2. To determine the final quantum number n f for the Balmer series. 3. To “attempt” to determine the initial and final quantum numbers for the electronic transition of Helium for the red, yellow, and purple emission lines by applying the Bohr Quantum Model. EQUIPMENT 1. Spectrometer (Figure 1) 2. Mercury light source 3. Hydrogen light source 4. Helium light source 5. Black cloth (to cover background light) 6. Diffraction grating 7. Bubble level
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2 Figure 1 - Spectrometer THEORY From your study of diffraction and interference you learned that the condition for interference maxima for a diffraction grating is given by θ λ sin d m = (2) where m is the order number, λ is the wavelength, and θ is the angle between the m th order and the central maxima. Bohr derived the expression = 2 2 2 1 1 1 i f n n RZ λ (1) from his quantum model. Initially he derived it for the hydrogen atom but extended it to other atoms in which all but one electron had been removed. Some examples are Li 2+ , Be 3+ and He + .
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3 EQUIPMENT SETUP Focusing the Spectrometer 1. Level the spectrometer by adjusting the three thumbscrews on the bottom of the table.
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