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2. Write the equation to calculate the energy levels for a hydrogen atom

2. Write the equation to calculate the energy levels for a hydrogen atom

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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5:33 * ll 79% i A5a prelab Spring 2022_1975968665 Name: Date: Course: Professor: A5a Prelab: Atomic Line Spectra and Energy Read the lab instructions before answering questions IMPORTANT 1. If you observe a photon of light with a wavelength A = 495 nm what is its frequency (use equation 1 from the lab)? 2. Write the equation to calculate the energy levels for a hydrogen atom 3. Calculate the energy levels for n = 1 to n = 7 En ר
Transcribed Image Text:5:33 * ll 79% i A5a prelab Spring 2022_1975968665 Name: Date: Course: Professor: A5a Prelab: Atomic Line Spectra and Energy Read the lab instructions before answering questions IMPORTANT 1. If you observe a photon of light with a wavelength A = 495 nm what is its frequency (use equation 1 from the lab)? 2. Write the equation to calculate the energy levels for a hydrogen atom 3. Calculate the energy levels for n = 1 to n = 7 En ר
5:37 P 79%i This document contains ink, shapes and im... Where : c = speed of light c = 2.99792458 x 108 m/s 2 = wavelength 1 = frequency Equation 1 C = lv Equation 2 E = v h Where : E = energy of the light v = frequency of the light h = Plank's constant h= 6.626 0693 x 10-34 Js 1.602 x 10-19 J = 1 eV (electron volt) Equation 3 En -13.6 (eV) Where n can be from 1 to 7 First, solve Equation 1 for the frequency of each of the lines obtained from your plot of the spectra of the hydrogen gas. Then, using Equation 2, it becomes possible to calculate energy of each line spectrum of the hydrogen gas. Notice that it is also necessary to convert the energies from joules to electron volts. Fill this information in to the appropriate spots on the Data Table. . In the last equation, Equation 3, you will use trial and error to find out which AE corresponds to the energies you have previously calculated. First, making use of the fact that n can go from 1 to 7, calculate the energies of each of the different orbits for a hydrogen atom. Fill these numbers into the Data Table. Next, you will need to look at the differences between one n and the next. Start by calculating the difference of the energy at n= 2 minus the energy of n = 1. Then calculate the energy at n= 3 minus the energy at n = 2. Continue with these calculations until you find a difference that corresponds to your calculated value for the first line spectrum of hydrogen. Once you have found which difference corresponds to your calculated energy, it is possible to decipher which emission series your emission spectrum corresponds with. Then calculate the subsequent differences between the energies at n for the rest of your series. For example: suppose you found that for your theoretical energies, the energy at n = 4 minus the energy at n = 3 matched up with your calculated first energy. This means that your first electron dropped from the 4t energy level to the 3rd energy level. This means that all subsequent calculated energies represent a drop from higher levels to the 3rd level. At this point you would want to confirm the rest of the energy drops match up with this series. Take the energy at n= 5 and subtract from it the energy at n = 3 to confirm that your E, calculated is the same as the energy emitted by an electron dropping from the 5th energy level to the 3rd energy level. Then take the energy for 7 = 6 and subtract n = 3 from it to compare your Ez calculation. After you have confirmed all of the drops in energy levels for your observed/calculated energies, you can now make your energy diagram. Your energy diagram should look something like the energy diagram below, only, instead of having multiple emission series on it, you will have only a single emission series. Once you have made your diagram compare it to the energy diagram offered below and identify the series. n = o. 0.00 ev n = 7 n = 6 -0.278 ev -0.378 ev n = 5 -0.544 ev Pfund n = 4 -0.85 ev Brackett n = 3 -1.511 ev Paschen n = 2 -3.40 ev Balmer n = 1 -13.6 ev Lyman Figure 5
Transcribed Image Text:5:37 P 79%i This document contains ink, shapes and im... Where : c = speed of light c = 2.99792458 x 108 m/s 2 = wavelength 1 = frequency Equation 1 C = lv Equation 2 E = v h Where : E = energy of the light v = frequency of the light h = Plank's constant h= 6.626 0693 x 10-34 Js 1.602 x 10-19 J = 1 eV (electron volt) Equation 3 En -13.6 (eV) Where n can be from 1 to 7 First, solve Equation 1 for the frequency of each of the lines obtained from your plot of the spectra of the hydrogen gas. Then, using Equation 2, it becomes possible to calculate energy of each line spectrum of the hydrogen gas. Notice that it is also necessary to convert the energies from joules to electron volts. Fill this information in to the appropriate spots on the Data Table. . In the last equation, Equation 3, you will use trial and error to find out which AE corresponds to the energies you have previously calculated. First, making use of the fact that n can go from 1 to 7, calculate the energies of each of the different orbits for a hydrogen atom. Fill these numbers into the Data Table. Next, you will need to look at the differences between one n and the next. Start by calculating the difference of the energy at n= 2 minus the energy of n = 1. Then calculate the energy at n= 3 minus the energy at n = 2. Continue with these calculations until you find a difference that corresponds to your calculated value for the first line spectrum of hydrogen. Once you have found which difference corresponds to your calculated energy, it is possible to decipher which emission series your emission spectrum corresponds with. Then calculate the subsequent differences between the energies at n for the rest of your series. For example: suppose you found that for your theoretical energies, the energy at n = 4 minus the energy at n = 3 matched up with your calculated first energy. This means that your first electron dropped from the 4t energy level to the 3rd energy level. This means that all subsequent calculated energies represent a drop from higher levels to the 3rd level. At this point you would want to confirm the rest of the energy drops match up with this series. Take the energy at n= 5 and subtract from it the energy at n = 3 to confirm that your E, calculated is the same as the energy emitted by an electron dropping from the 5th energy level to the 3rd energy level. Then take the energy for 7 = 6 and subtract n = 3 from it to compare your Ez calculation. After you have confirmed all of the drops in energy levels for your observed/calculated energies, you can now make your energy diagram. Your energy diagram should look something like the energy diagram below, only, instead of having multiple emission series on it, you will have only a single emission series. Once you have made your diagram compare it to the energy diagram offered below and identify the series. n = o. 0.00 ev n = 7 n = 6 -0.278 ev -0.378 ev n = 5 -0.544 ev Pfund n = 4 -0.85 ev Brackett n = 3 -1.511 ev Paschen n = 2 -3.40 ev Balmer n = 1 -13.6 ev Lyman Figure 5
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