hydragen. Rld= 2.18x 10-l8J. speed af feght = 3.0 Xl0°mb. こ4 calculcate the womelyth f the hynt ehitted ? フ

Chemistry
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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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**Transcription for Educational Website:**

---

**Problem Statement**

- **Electron Transition in Hydrogen:**
  - Initial Energy Level \( n = 8 \)
  - Final Energy Level \( n = 4 \)

- **Constants:**
  - \( R_H = 2.18 \times 10^{-18} \, \text{J} \) (Rydberg constant for hydrogen)
  - Speed of light \( = 3.0 \times 10^8 \, \text{m/s} \)

**Task:**
Calculate the wavelength of the light emitted during this transition.

---

**Explanation for Calculation:**

To find the wavelength of light emitted when an electron transitions between two energy levels in a hydrogen atom, use the following formula derived from 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 of light emitted,
- \( R_H \) is the Rydberg constant,
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final energy levels respectively.

**Application:**
Substitute the given values of \( n_1 = 4 \) and \( n_2 = 8 \) and solve for \( \lambda \).

Following this, use the relationship between frequency (\( f \)), speed of light (\( c \)), and wavelength (\( \lambda \)):

\[
\lambda = \frac{c}{f}
\]

Where:
- \( c = 3.0 \times 10^8 \, \text{m/s} \)

This calculation will provide the wavelength of the emitted light in meters.
Transcribed Image Text:**Transcription for Educational Website:** --- **Problem Statement** - **Electron Transition in Hydrogen:** - Initial Energy Level \( n = 8 \) - Final Energy Level \( n = 4 \) - **Constants:** - \( R_H = 2.18 \times 10^{-18} \, \text{J} \) (Rydberg constant for hydrogen) - Speed of light \( = 3.0 \times 10^8 \, \text{m/s} \) **Task:** Calculate the wavelength of the light emitted during this transition. --- **Explanation for Calculation:** To find the wavelength of light emitted when an electron transitions between two energy levels in a hydrogen atom, use the following formula derived from 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 of light emitted, - \( R_H \) is the Rydberg constant, - \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final energy levels respectively. **Application:** Substitute the given values of \( n_1 = 4 \) and \( n_2 = 8 \) and solve for \( \lambda \). Following this, use the relationship between frequency (\( f \)), speed of light (\( c \)), and wavelength (\( \lambda \)): \[ \lambda = \frac{c}{f} \] Where: - \( c = 3.0 \times 10^8 \, \text{m/s} \) This calculation will provide the wavelength of the emitted light in meters.
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