Why Is the Calculated Wavelength Incorrect in This Hydrogen Atom Problem?

The deBroglie wavelength is given by λ = h/p, where p is the momentum of the electron. In summary, when trying to calculate the energy of an electron in the first excited state of a hydrogen atom, it is important to use the correct formula and to clarify what is being asked for, as confusion can arise when using the incorrect units. In this case, the correct formula for finding the wavelength of the photon emitted in the transition from the first excited state to the ground state is λ = hc/E, where E is the energy difference between the two states.
  • #1
Suyash Singh

Homework Statement


Calculate energy of electron in first excited state of hydrogen atom.

Homework Equations


n=2
when i use E=-13.6 (z/n)^2
and then use E=hc/lamda(wavelength)
then wavelength is coming wrong

The Attempt at a Solution


the correct answer is 6.68 armstrong.
 
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  • #2
Ångström (not armstrong) is a unit of length, not a unit of energy. It is likely that you are not being asked what you have stated that you are being asked about here. The question is likely what the wavelength of the photon emitted when the electron in the first excited state of hydrogen transits to the ground state. This is not the same thing as the energy in the first excited state.
 
  • #3
Suyash Singh said:
when i use E=-13.6 (z/n)^2
and then use E=hc/lamda(wavelength)
then wavelength is coming wrong
Are you trying to find the deBroglie wavelength of the electron when it is in the first excited state? If so, the formula E = hc/λ is not the correct formula.
 

Related to Why Is the Calculated Wavelength Incorrect in This Hydrogen Atom Problem?

1. What is the Bohr orbit?

The Bohr orbit, also known as the Bohr model, is a simplified model of the electron's movement around the nucleus in an atom. It was proposed by Danish physicist Niels Bohr in 1913 and is based on the idea that electrons orbit the nucleus in specific energy levels, or shells, and can jump between these levels by absorbing or emitting energy.

2. How does the Bohr orbit differ from the modern atomic model?

The Bohr orbit is a simplified version of the modern atomic model, which is based on quantum mechanics. In the modern model, the electron's position cannot be precisely determined, and it is described by a probability distribution rather than a definite orbit. Additionally, the modern model includes more complex energy levels and sublevels, whereas the Bohr model only has a few discrete energy levels.

3. What is the significance of the Bohr orbit?

The Bohr orbit was a significant development in the understanding of atomic structure and helped to explain the spectra of atoms. It also laid the foundation for further advancements in quantum mechanics and our understanding of the behavior of electrons in atoms.

4. How does the Bohr orbit explain the stability of atoms?

The Bohr orbit explains the stability of atoms by proposing that electrons can only occupy specific energy levels, and they do not emit energy while in these stable levels. This idea was revolutionary at the time, as it contradicted classical physics, which suggested that orbiting electrons should continuously lose energy and eventually spiral into the nucleus.

5. Can the Bohr orbit be used to accurately predict the behavior of all atoms?

No, the Bohr orbit is a simplified model and does not accurately predict the behavior of all atoms. It works well for atoms with only one electron, such as hydrogen, but fails to explain more complex atoms. The modern atomic model is a more accurate description of atomic behavior and is used to predict the behavior of all atoms.

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