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The question you uploaded seems to be written in Icelandic, and it asks about the type of light (likely referring to wavelength or frequency) that can excite an electron in a hydrogen atom from the ground state (\(n=1\)) to the third energy level (\(n=3\)). It mentions "absorption of light" (Gleypni ljós).

This question relates to the concept of electron transitions in hydrogen atoms, which are governed by the Rydberg formula for the energy differences between different energy levels:

\[
\Delta E = E_3 - E_1 = -\frac{13.6 \, \text{eV}}{n_3^2} + \frac{13.6 \, \text{eV}}{n_1^2}
\]

Where \(n_1\) and \(n_3\) are the initial and final energy levels, respectively. We are given \(n_1 = 1\) and \(n_3 = 3\).

The energy absorbed corresponds to the energy of the photon, which can be related to the wavelength by:

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

Where:
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(\lambda\) is the wavelength.

Let me calculate the energy difference and the corresponding wavelength of the photon that would be absorbed to move the electron from \(n=1\) to \(n=3\).The energy required to excite an electron in a hydrogen atom from \(n=1\) to \(n=3\) is approximately 12.09 eV. This corresponds to a photon with a wavelength of about 102.63 nanometers (nm), which falls in the ultraviolet (UV) range of the electromagnetic spectrum.

Would you like more details on this process or have any other questions?

Here are 5 related questions you might explore:
1. What are the energy levels in a hydrogen atom, and how are they calculated?
2. What is the Rydberg formula, and how is it used in atomic physics?
3. How do electron transitions produce spectral lines in different regions (visible, UV, etc.)?
4. What is the significance of the ultraviolet light in atomic transitions?
5. How does the energy of photons relate to wavelength and frequency?

**Tip:** The wavelength of light decreases as the energy of the photon increases, with ultraviolet photons being more energetic than visible light photons.

Hverskonar ljós er líklegast til að koma rafeind vetnisatóm úr skammtabrepi n=1 upp í skammtabrep n=3? (Gleypni ljós)

Explore how a photon excites an electron in a hydrogen atom from energy level n=1 to n=3, including calculations of the energy difference and the corresponding wavelength of light absorbed.

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