Calculate the wavelength of light associated with the transition from n=1 to n-3 in the hydrogen atom in nanometers. 971 nm 136 nm 155 nm 646 nm 103 nm Next >
Calculate the wavelength of light associated with the transition from n=1 to n-3 in the hydrogen atom in nanometers. 971 nm 136 nm 155 nm 646 nm 103 nm Next >
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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![### Hydrogen Atom Wavelength Transition Calculation
Calculate the wavelength of light associated with the transition from \( n = 1 \) to \( n = 3 \) in the hydrogen atom in nanometers.
**Options:**
- \( O \ 971 \ nm \)
- \( O \ 136 \ nm \)
- \( O \ 155 \ nm \)
- \( O \ 646 \ nm \)
- \( O \ 103 \ nm \)
*[Next >]*
In this problem, you are asked to determine the wavelength of the emitted or absorbed light during the transition of an electron between energy levels in a hydrogen atom. The energy levels are denoted by the principal quantum number \( n \).
To solve this, you would typically use the Rydberg formula for hydrogen:
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where:
- \( \lambda \) is the wavelength,
- \( R_H \) is the Rydberg constant (\( 1.097 \times 10^7 \ \text{m}^{-1} \)),
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the energy levels involved (\( n \) where \( n_2 > n_1 \)).
In this case, \( n_1 = 1 \) and \( n_2 = 3 \). The calculated wavelength from this interaction will fall into one of the provided multiple choice options in nanometers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30d9daac-bb71-46b3-af88-60b407cbaed8%2Ffb619e10-a840-48c7-a0c7-721b1255d1a3%2Flxdwcel_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Hydrogen Atom Wavelength Transition Calculation
Calculate the wavelength of light associated with the transition from \( n = 1 \) to \( n = 3 \) in the hydrogen atom in nanometers.
**Options:**
- \( O \ 971 \ nm \)
- \( O \ 136 \ nm \)
- \( O \ 155 \ nm \)
- \( O \ 646 \ nm \)
- \( O \ 103 \ nm \)
*[Next >]*
In this problem, you are asked to determine the wavelength of the emitted or absorbed light during the transition of an electron between energy levels in a hydrogen atom. The energy levels are denoted by the principal quantum number \( n \).
To solve this, you would typically use the Rydberg formula for hydrogen:
\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where:
- \( \lambda \) is the wavelength,
- \( R_H \) is the Rydberg constant (\( 1.097 \times 10^7 \ \text{m}^{-1} \)),
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the energy levels involved (\( n \) where \( n_2 > n_1 \)).
In this case, \( n_1 = 1 \) and \( n_2 = 3 \). The calculated wavelength from this interaction will fall into one of the provided multiple choice options in nanometers.
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