Calculate the wavelength of the photon emitted when an electron makes a transition from n=6�=6 to n=3�=3. You can make use of the following constants:

h=6.626×10−34 J⋅sℎ=6.626×10−34 J⋅s

c=2.998×108 m/s�=2.998×108 m/s

1 m=109 nm1 m=109 nm

Express your answer to four significant figures and include the appropriate units.

To calculate the wavelength of the photon emitted during an electron transition from \( n = 6 \) to \( n = 3 \) in a hydrogen atom, we can use the **Rydberg formula**:

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

where:
- \( \lambda \) is the wavelength of the emitted photon.
- \( R \) is the Rydberg constant, \( R = 1.097 \times 10^7 \, \text{m}^{-1} \).
- \( n_1 \) and \( n_2 \) are the initial and final energy levels of the electron, respectively.

Given:
- \( n_1 = 6 \)
- \( n_2 = 3 \)

We first calculate the frequency of the photon using the energy difference, then convert it to wavelength using the speed of light equation \( c = \lambda \nu \).

Let's plug in the values and compute the wavelength.The wavelength of the photon emitted during the transition from \( n = 6 \) to \( n = 3 \) is approximately **1093.9 nm** (nanometers).

Would you like more details or have any questions? Here are five related questions to explore further:

1. What is the significance of the Rydberg constant in quantum mechanics?
2. How does the energy difference between electron levels relate to photon emission?
3. Can this wavelength fall within the visible spectrum?
4. How would the wavelength change if the electron transitioned from \( n = 5 \) to \( n = 3 \)?
5. What is the relationship between photon wavelength and energy?

**Tip:** The energy of a photon is inversely proportional to its wavelength, meaning shorter wavelengths correspond to higher energy photons.

Calculate the wavelength of the photon emitted when an electron makes a transition from n=6 to n=3. You can make use of the following constants: h=6.626×10−34 J⋅s, c=2.998×108 m/s, 1 m=109 nm. Express your answer to four significant figures and include the appropriate units.

Learn how to calculate the wavelength of a photon emitted when an electron transitions from n=6 to n=3 using quantum mechanics concepts. The solution involves the Rydberg formula and constants such as Planck's constant and the speed of light. Suitable for Grades 11-12.

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