Hydrogen Wave Function

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Hydrogen Wave Function In this essay we will discuss six possible quantum states of the Hydrogen atom. Each quantum state will have a corresponding plot printout and all information will reflect the outline given on page 5 of our Physics 100 Homework and Lecture Notes Booklet. We will use the convention that yellow = positive(+) and blue = negative(-) for color coding purposes on angular, radial and density plots (printouts). The first quantum number (n) is called the principle quantum number and represents the total energy of the atom. The second quantum number (l) is known as the angular quantity and is responsible for the shape of possible electron orbits. The third quantum number is the magnetic number and is represented on the z axis in three dimensions. Case one: Ground state = (n,l,m) = (1,0,0) . The ground state is the least possible energy state in which the hydrogen atom can maintain its electron orbit. Looking at the density plot of the ground state shows a yellow sphere, which indicates a positive charge. The density plot agrees with the l = 0 diagram in our homework manual. The angular quantum number l = 0, gives rise to 2(l) =2(0) = 0 angular lobes. This means there are no angular standing waves in the 360 degree periodic process. The ground state also has no radial nodes since [n-l-1] = [1-0-1] =0. Looking at the radial plot also confirms 0 nodes, as the graph approaches positive infinity on the x axis the graph converges to 0 (does not intersect the x axis). There is one radial lobe since [n-l] = [1=0] = 1 which corresponds to 1 standing wave train along the radial path. The density plot is about the same size and shape of the angular plot. The yellow color of the density plot is in agreement with the angular and radial plots. The tunnel effect or fuzziness of the density plot appears toward the edges of the ball shape as the radius increases

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