Lab7 Report

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Georgia Institute Of Technology *

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1310

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Chemistry

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Oct 30, 2023

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Uploaded by ProfessorOwlMaster973

Quantum Mechanics of Light and the Atom 8 March 2023 CHEM 1310 Laboratory Data and Results ☐ Table 1. Distance measurements for diffraction of red and green laser light. Red light (633 nm) D (cm) y 1 (cm) Calculated d (μm) 100.0 37.4 1.81 100.0 36.9 1.83 100.0 37.0 1.82 Mean d (μm) 1.82 Standard deviation of d (μm) 0.01 Green light (532 nm) D (cm) y 1 (cm) Calculated d (μm) 100.0 25.0 2.19 100.0 25.4 2.16 100.0 24.5 2.24

☐ Figure 1. Kinetic energy of ejected electrons as a function of inverse wavelength in the photoelectric effect of metals. Figure 1.1 Copper Figure 1.2 Sodium y = 1219.6x - 4.6674 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 0.00000 0.00200 0.00400 0.00600 0.00800 0.01000 0.01200 Maximum KE of Ejected Copper Electrons (J) Inverse Wavelength of Light (1/nm) y = 1222.6x - 2.254 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 0.00000 0.00050 0.00100 0.00150 0.00200 0.00250 0.00300 0.00350 Maximum KE of Ejected Sodium Electrons(J) Inverse Wavelength of Light (1/nm)

☐ Figure 2. Energy levels of the hydrogen atom as a function of 1/ n 2 . ☐ Figure 3. Visible emission spectrum of Helium. Color Of Line Wavelength (nm) Blue 440 Cyan 465 Light Green 485 Green 490 Orange 583 ☐ Figure 4. Visible emission spectrum of Neon. Color Of Line Wavelength (nm) Green 540 Yellow 570-600 Orange 600-620 Red 620-680 y = 456.81x - 88.767 R² = 0.9153 -90.0 -80.0 -70.0 -60.0 -50.0 -40.0 -30.0 -20.0 -10.0 0.0 0.000 0.020 0.040 0.060 0.080 0.100 0.120 Hydrogenic Energy Level (eV) Inverse Wavelength of Emitted Photons (1/nm)

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Discussion In part one of the experiment, the goal of our experimentation was to determine the distance between grooves in the diffraction grating, notated as ‘d’. To do this, we first started with the equation 𝜆 ? = 𝑦 √𝑦 2 +𝐷 2 , if we solve this equation for ‘d’, we find that 𝑑 = 𝜆√𝑦 2 +𝐷 2 𝑦 . Now, if we take trial one for the red laser, where D= 100 cm, y= 37.4 cm, and 𝜆 = 633 nm, we can calculate ‘d’ in nm. Next, we divide ‘d’ by 1000 to convert it to micrometers, and we’re left with d= 1.81 micrometers. The precision of this calculation can be reported to two decimal places, as the fewest number of significant figures present in the data it originates from is 3. Additionally, the standard deviation is accurate to hundredths (stdev= 0.01) therefore, the mean is accurate up to two decimal places In part two of this experiment, we determined the maximum kinetic energies of various ejected electrons as wavelength was changed. As shown by the data, as the inverse of the wavelength increased, so did the maximum kinetic energy of the electrons ejected (wavelength decrease = kinetic energy increase). For instance, at an inverse wavelength of 0.0039, copper ejected electrons with kinetic energy of 0.15 eV, and at an inverse wavelength of 0.0056, copper ejected electrons with kinetic energy of 2.30 eV. This agrees with the equation relating wavelength to photon energy 𝜆𝑉 = 𝐶 where 𝜆 = wavelength, V= frequency of the particle, and C= the speed of light (3e10 m/s). In this equation, as wavelength decreases, frequency increases, and as frequency increases, the energy being transferred into the emitted electrons from the copper increases as well. This is because as frequency is increased, energy of a photon increases according to the equation 𝐸 = ℎ𝑉 where h= Planck’s Constant (6.626e-34 J*s). Using the data from part three of this experiment, we determined energy levels for specific wavelengths of light. One of these levels ,n=1 in hydrogen, has an energy value that can be calculated using the equation −13.6 ?𝑉 ? 2 where n=1 because we’re looking at the first quantum energy level. Therefore, n=1 has an energy level of -13.6 eV. Using this same equation, we can then create a model for the energy levels of different wavelengths emitted by hydrogen. First, we calculate the energy level of each quantum energy level (n=6,5,4,3,2). Next, we can model the emission of photons from energy levels 6 through 3 to energy level 2. By following the equation 𝐸 𝑃ℎ?𝑡?? = 𝐸 ?? − 𝐸 ?𝑖 , we can calculate a photon energy for each of the emissions present in a hydrogen atom. Next, we can compare these values to the energy levels found by converting the

observed wavelengths of hydrogen emission (using the equation 𝐸 ?ℎ?𝑡?? = − ℎ? 𝜆 . When we compare these values, we find that the jump from 6-2 correlates to the deep violet emission line, 5-2 is deep blue, 4-2 is blue-green, and 3-2 is red. This logically makes sense, as the wavelength of the observed emission line decreases as the energy change between each level increases. Additionally, the most high-power energy change is purple, which follows traditional visible light spectra where violet is the highest energy visible light. The described model can be found here: ☐ Figure 5. Energy levels of a hydrogen atom and associated color emissions

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