Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from n = 6 to n = 1. energy emitted:

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...
icon
Related questions
Question

I couldn't fit both parts of the question into one picture so please answer both sections. Thank you. 

**Photon Emission in Hydrogen Atom Transition**

Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from \( n = 6 \) to \( n = 1 \).

**Energy Emitted:**

[Text Box for Input] \( \text{J} \)

---

This process involves using the Rydberg formula to calculate the photon energy released during the electron transition. The energy associated with the transition can be calculated using the formula: 

\[ E = -R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

Where:
- \( E \) is the energy of the photon emitted,
- \( R_H \) is the Rydberg constant (\(2.18 \times 10^{-18}\) J),
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final states. Here, \( n_1 = 1 \) and \( n_2 = 6 \).

When an electron falls to a lower energy level, it releases energy in the form of a photon, which can be quantified using this formula.
Transcribed Image Text:**Photon Emission in Hydrogen Atom Transition** Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from \( n = 6 \) to \( n = 1 \). **Energy Emitted:** [Text Box for Input] \( \text{J} \) --- This process involves using the Rydberg formula to calculate the photon energy released during the electron transition. The energy associated with the transition can be calculated using the formula: \[ E = -R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \] Where: - \( E \) is the energy of the photon emitted, - \( R_H \) is the Rydberg constant (\(2.18 \times 10^{-18}\) J), - \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final states. Here, \( n_1 = 1 \) and \( n_2 = 6 \). When an electron falls to a lower energy level, it releases energy in the form of a photon, which can be quantified using this formula.
**Problem Statement**

Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level \( n = 7 \) to the level \( n = 1 \).

\[ \lambda = \boxed{} \, \text{nm} \]
Transcribed Image Text:**Problem Statement** Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level \( n = 7 \) to the level \( n = 1 \). \[ \lambda = \boxed{} \, \text{nm} \]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY