Find the wavelength (in nm) of a photon whose energy is 4.90 × 10-1⁹ J.

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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**Problem Statement:**

Find the wavelength (in nm) of a photon whose energy is \(4.90 \times 10^{-19}\) J.

**Input Fields:**

- **Number:** [Input box for the calculated wavelength value]
- **Units:** [Dropdown menu for selecting units]

**Additional Resources:**

- **eTextbook and Media:** [Link/Section for further reading and media resources]

**Explanation:**

To find the wavelength of the photon given its energy, use the formula derived from the Planck-Einstein relation:

\[
E = \frac{hc}{\lambda}
\]

Where:
- \(E\) is the energy of the photon (\(4.90 \times 10^{-19}\) J in this case).
- \(h\) is the Planck’s constant (\(6.626 \times 10^{-34}\) Js).
- \(c\) is the speed of light in a vacuum (\(3.00 \times 10^8\) m/s).
- \(\lambda\) is the wavelength in meters.

Rearrange the formula to solve for the wavelength (\(\lambda\)):

\[
\lambda = \frac{hc}{E}
\]

After calculating \(\lambda\) in meters, convert it to nanometers (1 m = \(10^9\) nm).

**Note:** Fill in the calculated value in the provided input box and specify the correct unit using the dropdown menu.
Transcribed Image Text:**Problem Statement:** Find the wavelength (in nm) of a photon whose energy is \(4.90 \times 10^{-19}\) J. **Input Fields:** - **Number:** [Input box for the calculated wavelength value] - **Units:** [Dropdown menu for selecting units] **Additional Resources:** - **eTextbook and Media:** [Link/Section for further reading and media resources] **Explanation:** To find the wavelength of the photon given its energy, use the formula derived from the Planck-Einstein relation: \[ E = \frac{hc}{\lambda} \] Where: - \(E\) is the energy of the photon (\(4.90 \times 10^{-19}\) J in this case). - \(h\) is the Planck’s constant (\(6.626 \times 10^{-34}\) Js). - \(c\) is the speed of light in a vacuum (\(3.00 \times 10^8\) m/s). - \(\lambda\) is the wavelength in meters. Rearrange the formula to solve for the wavelength (\(\lambda\)): \[ \lambda = \frac{hc}{E} \] After calculating \(\lambda\) in meters, convert it to nanometers (1 m = \(10^9\) nm). **Note:** Fill in the calculated value in the provided input box and specify the correct unit using the dropdown menu.
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