Zhikai AtomicSpectra - PC1222 Lab Report: Atomic Spectra|...

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PC1222 Lab Report: Atomic Spectra|| ||Wang Zhikai|| ||A0080959N|| ||Group B6|| 1 Objectives To investigate if the visible light wavelengths of hydrogen as predicted by Bohr’s theory agree with the experimental values. To determine an experimental value for the Rydberg constant using a fit of the measured values of hydrogen wavelengths to the Balmer equation. To identify the two unknown elements by their visible optical spectra using earlier obtained results. 2 Introduction The hot gas of an element produces a spectrum that consists of discrete wavelengths. These wavelengths are related to the orbit of the element, n by the following equation: , where is known as the Rydberg constant, represents the wavelength and n is an integer of successive values greater than 2. In order to explain this relationship, Neils Bohr came up with a theory involving the following concepts. Bohr postulates that electrons move in circular orbits of radius r n around the nucleus due to the effect of the Coulomb force between the positive nucleus and the negative electrons. The electron with mass m can only have velocity v n and orbits r n that satisfy the relationship mr n v n = nh/2π where h = 6.626 * 10 -34 Js and n = 1,2,3,4,…. In an allowed orbit, the electron does not radiate energy and the atom is stable in these orbits; this is called a stationary state. The atom radiates energy only when an electron makes a transition from one allowed orbit to another allowed orbit. Therefore, the energy of the nth level E n can be described by the equation , where m represents the mass of an electron, e represents the charge of an electron and is the electrical permittivity of free space. The energy radiated by the atom when the electron makes a transition is related to the wavelength of the photon and the orbit n of the electron by the following equation: This expression can be used to obtain Balmer’s equation of , if we replace with . In this experiment, wavelengths will be measured with a diffraction grating spectrometer. Images of the slit for different wavelengths will then appear in the first order, thus following the equation , where d is the grating spacing and is the angle measured. Measurements of the angle will therefore provide us with d from the mercury spectrum. Using this value of the grating spacing, measurements of the angles at which the hydrogen wavelengths occur can allow us to determine the respective wavelengths. 3 Methodology Part A, B and C all involve the usage of the same diffraction grating spectrometer, albeit with different gases in the discharge tubes. We adjusted the telescope before measurements were taken to obtain a sharp image of the slit when the discharge tube is placed close to the end of the collimator. We then placed the diffraction grating in between the collimator tube and the telescope tube with the grating perpendicular to the collimator tube. Part A: Mercury Spectrum
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Zhikai AtomicSpectra - PC1222 Lab Report: Atomic Spectra|...

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