Calculating Energy Levels and Wavelengths in the Hydrogen Atom

In summary, the conversation discusses the transition of an electron in a hydrogen atom from the n = 1 to n = 4 energy level. The electron's change in energy is 12.75 eV and the transition is from a lower to a higher energy level. The wavelength of the emitted or absorbed photon is approximately 9.74 x 10^-8 m.
  • #1
Kennedy111
27
0

Homework Statement


In the hydrogen atom, the electron jumps from the n = 1 level to the n = 4 level.
a. During this transition from n = 1 to n = 4, is a photon emitted or absorbed?
b. What is the change in energy of the electron?
c. State the transition in words.
d. What is the wavelength of the emitted or absorbed photon?

Energy when n = 1 : -13.6 eV
Energy when n = 4 : -0.85 eV

Homework Equations


ΔE = Ef - Ei
λ = hc/E


The Attempt at a Solution


a. I believe I understand this question. I would say that the photon is absorbed...
b. ΔE = Ef - Ei
ΔE = (-0.85 eV) - (-13.6 eV)
= 12.75 eV
c. The electron has made a transition from the n = 1 to the n = 4 energy level.. is that it?? I feel like this question was too easy...
d. I used λ = hv/E but I'm not sure if that was the right formula to use...
λ = (4.14 x 10^-15 eV*s)(3.00 x 10^8 m/s) / (12.75 eV)
= 9.74 x 10^-8 m

I am just unsure of my work and would really like a second opinion. Thank you!
 
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  • #2
To simplify the calculations in d, you can equate hc=1240 eV nm. Rest everything seems ok to me. (I haven't checked your calculations.)
 

Related to Calculating Energy Levels and Wavelengths in the Hydrogen Atom

1. What are energy levels in an atom?

Energy levels in an atom refer to the specific amounts of energy that an electron can have while orbiting the nucleus. These energy levels are represented by the electron's distance from the nucleus, with the lowest energy level being the closest to the nucleus.

2. How do energy levels relate to wavelengths?

The energy level of an electron determines the wavelength of light that it can absorb or emit. When an electron moves from a higher energy level to a lower one, it releases energy in the form of light with a specific wavelength. The difference in energy levels between the electron's initial and final state determines the wavelength of the light.

3. What is the relationship between energy levels and the electromagnetic spectrum?

The electromagnetic spectrum is a range of wavelengths, from radio waves to gamma rays. Each type of electromagnetic radiation corresponds to a specific amount of energy. As an electron moves between energy levels, it emits or absorbs photons with specific wavelengths that fall within the electromagnetic spectrum.

4. Can energy levels and wavelengths be measured?

Yes, energy levels and wavelengths can be measured using various scientific instruments. For example, a spectrophotometer can measure the wavelengths of light absorbed or emitted by a substance, which can then be used to determine the energy levels of the electrons within that substance.

5. How do energy levels and wavelengths impact the colors we see?

The colors we see are a result of different wavelengths of light being absorbed or reflected by objects. The energy levels of the electrons within an object determine which wavelengths of light it can absorb and which it reflects. This is why objects appear to have different colors - they are absorbing and reflecting different wavelengths of light.

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