Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the A transition from the energy level n = 4 to the level n = 2. λ =
Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the A transition from the energy level n = 4 to the level n = 2. λ =
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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Question
![**Calculate the Wavelength of a Spectral Line in a Hydrogen Atom**
*Objective:* Determine the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom transitions from the energy level \( n = 4 \) to the level \( n = 2 \).
\[
\lambda = \boxed{\hspace{10cm}}
\]
*Unit:* nm (nanometers)
**Additional Information:**
- This problem involves the calculation of the wavelength using energy level transitions in a hydrogen atom.
- The transition mentioned is from the fourth energy level to the second, which is typically associated with the Balmer series in spectroscopy.
**Instructions:**
- Calculate the energy difference between the energy levels \( n = 4 \) and \( n = 2 \).
- Use the Rydberg formula to determine the wavelength of light emitted during this electron transition.
- Equation: \(\frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)\)
- Where \( R_H \) is the Rydberg constant (\(1.097 \times 10^7 \, \text{m}^{-1}\))
- \( n_1 = 2 \) and \( n_2 = 4 \)
**Diagrams:**
No diagrams or graphs are present in this prompt.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa488a3d5-fb60-4389-a69a-9fdfd1297bd5%2Fa4b0b1f9-7441-43bd-b9b3-7f8df2046541%2F7fvybzx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculate the Wavelength of a Spectral Line in a Hydrogen Atom**
*Objective:* Determine the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom transitions from the energy level \( n = 4 \) to the level \( n = 2 \).
\[
\lambda = \boxed{\hspace{10cm}}
\]
*Unit:* nm (nanometers)
**Additional Information:**
- This problem involves the calculation of the wavelength using energy level transitions in a hydrogen atom.
- The transition mentioned is from the fourth energy level to the second, which is typically associated with the Balmer series in spectroscopy.
**Instructions:**
- Calculate the energy difference between the energy levels \( n = 4 \) and \( n = 2 \).
- Use the Rydberg formula to determine the wavelength of light emitted during this electron transition.
- Equation: \(\frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)\)
- Where \( R_H \) is the Rydberg constant (\(1.097 \times 10^7 \, \text{m}^{-1}\))
- \( n_1 = 2 \) and \( n_2 = 4 \)
**Diagrams:**
No diagrams or graphs are present in this prompt.
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