Wavelength of a photon

In summary: So it would be the largest jump, from n=inf to n=1. In summary, the shortest wavelength photon emitted by a hydrogen atom occurs when an electron jumps from the infinite energy level to the n=1 energy level, with a wavelength of approximately 9.13 x 10^-8 m. The photon energy is 13.6 eV.
  • #1
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Homework Statement


Calculate the shortest wavelength photon that is emitted in the hydrogen atom.

Energy when n = 1 = -13.6 eV

Homework Equations



E = hc/λ
λ = hc/E

The Attempt at a Solution


Well as far as I understand, when the electron is in the n = 1 energy level it has it's lowest energy, which is -13.6 eV. I believe this is where the shortest wavelength will be...
λ = hc/E
= (4.14 x 10^-15 eV*s)(3.00 x 10^8 m/s) / -13.6 eV
= approx 9.13 x 10^-8 m

Was my method correct? I would really just like a second opinion. Thank you!
 
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  • #2
The method is correct, but the photon energy is positive: 13.6 eV, the same the electron loses when it becomes bounded to the hydrogen atom. You divided by -13.6 eV, then ignored the sign, which is wrong.

ehild
 
  • #3
Are n't photons produced when an electron jumps between energy levels not stay on one level? The shortest wavelength photon will be the one with least energy produced by an electron transition of the smallest energy. If the electron is to end up at n=1, the shortest wavelength photon comes from a jump from n=2 to n=1 (-3.4eV to -13.6eV).
 
  • #5
Sorry I have just realized my mistake. Shortest wavelength comes from the largest energy not the smallest.
 

1. What is the wavelength of a photon?

The wavelength of a photon is the distance between two consecutive peaks or troughs of the wave it travels in. It is usually measured in meters (m) or nanometers (nm).

2. How is the wavelength of a photon related to its energy?

The wavelength of a photon and its energy are inversely proportional. This means that as the wavelength increases, the energy decreases and vice versa. This relationship is described by the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

3. Can the wavelength of a photon be measured?

Yes, the wavelength of a photon can be measured using various techniques such as diffraction grating, interferometry, or spectroscopy. These methods allow scientists to accurately determine the wavelength of a photon and study its properties.

4. What factors affect the wavelength of a photon?

The wavelength of a photon is primarily determined by its energy, which is determined by its frequency. Other factors that can affect the wavelength include the medium through which the photon is traveling, the temperature of the medium, and the presence of any electromagnetic fields.

5. Why is the wavelength of a photon important in scientific research?

The wavelength of a photon is important in scientific research because it helps us understand the behavior and properties of light. It is also a crucial factor in many areas of science, including optics, quantum mechanics, and astrophysics. Additionally, studying the wavelength of a photon can provide valuable insights into the nature of matter and the universe.

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