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The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula: R E=- n In this equation R, stands for the Rydberg energy, and n stands for the principal quantum number of the orbital that holds the electron. (You can find the value of the Rydberg energy using the Data button on the ALEKS toolbar.) Calculate the wavelength of the line in the emission line spectrum of hydrogen caused by the transition of the electron from an orbital with n= 12 to an orbital with n=8. Round your answer to 3 significant digits. um X 5

The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula: R E=- n In this equation R, stands for the Rydberg energy, and n stands for the principal quantum number of the orbital that holds the electron. (You can find the value of the Rydberg energy using the Data button on the ALEKS toolbar.) Calculate the wavelength of the line in the emission line spectrum of hydrogen caused by the transition of the electron from an orbital with n= 12 to an orbital with n=8. Round your answer to 3 significant digits. um X 5

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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The text details how to calculate the energy \( E \) of an electron in a hydrogen atom using the Bohr formula: \[ E = \frac{-R_y}{n^2} \] In this equation, \( R_y \) stands for the Rydberg energy, and \( n \) represents the principal quantum number of the orbital that contains the electron. (The value of the Rydberg energy can be found using the Data button on the ALEKS toolbar.) The task is to calculate the wavelength of the line in the emission spectrum of hydrogen caused by the transition of the electron from an orbital with \( n = 12 \) to an orbital with \( n = 8 \). The answer should be rounded to three significant digits. Below this, there's a space for inputting the result in micrometers (\(\mu m\)), with a set of interactive buttons to adjust and submit the answer. No graphs or diagrams are present.
Transcribed Image Text:The text details how to calculate the energy \( E \) of an electron in a hydrogen atom using the Bohr formula: \[ E = \frac{-R_y}{n^2} \] In this equation, \( R_y \) stands for the Rydberg energy, and \( n \) represents the principal quantum number of the orbital that contains the electron. (The value of the Rydberg energy can be found using the Data button on the ALEKS toolbar.) The task is to calculate the wavelength of the line in the emission spectrum of hydrogen caused by the transition of the electron from an orbital with \( n = 12 \) to an orbital with \( n = 8 \). The answer should be rounded to three significant digits. Below this, there's a space for inputting the result in micrometers (\(\mu m\)), with a set of interactive buttons to adjust and submit the answer. No graphs or diagrams are present.
Expert Solution
Step 1: Determine the wave length of a line from the given data:

Given,

the formula for energy of a electron in a hydrogen atom:

           E = fraction numerator negative R subscript y over denominator n squared end fraction

Initial orbital, n = 12 and the final orbital, n =8

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