The Hydrogen Atom: Photon Energy of n=4 to n=3 Transition

In summary, the n=4 to n=3 transition in the hydrogen atom is significant because it corresponds to the emission or absorption of a photon with a specific energy, known as the Lyman-alpha line. The energy of the photon can be calculated using the Rydberg formula and is influenced by factors such as temperature and external fields. This transition is related to the Bohr model of the hydrogen atom, and can also occur in other atoms, such as helium, with different resulting photon energies.
  • #1
UrbanXrisis
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What is the energy of the photon when the Hydrogen aton transitions from the n=4 to n=3 energy state?
 
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  • #2
UrbanXrisis said:
What is the energy of the photon when the Hydrogen aton transitions from the n=4 to n=3 energy state?

It has E = E4 - E3 because energy is conserved.

Use the Bohr energy level equation to find the indiviual level values
 
  • #3


The energy of a photon emitted during the transition of a hydrogen atom from the n=4 to n=3 energy state can be calculated using the Rydberg formula:

E = -Rhc(1/n1^2 - 1/n2^2)

Where E is the energy of the photon, R is the Rydberg constant (1.097x10^-2 nm^-1), h is Planck's constant (6.626x10^-34 J*s), and c is the speed of light (2.998x10^8 m/s).

Plugging in the values for n1=4 and n2=3, we get:

E = -((1.097x10^-2 nm^-1)(6.626x10^-34 J*s)(2.998x10^8 m/s))(1/4^2 - 1/3^2)

= -2.178x10^-18 J

Therefore, the energy of the photon emitted during the n=4 to n=3 transition is 2.178x10^-18 J. This corresponds to a wavelength of approximately 911.7 nm, which falls within the infrared region of the electromagnetic spectrum.
 

1. What is the significance of the n=4 to n=3 transition in the hydrogen atom?

The n=4 to n=3 transition in the hydrogen atom is significant because it corresponds to the emission or absorption of a photon with a specific energy. This energy, known as the Lyman-alpha line, falls in the ultraviolet region of the electromagnetic spectrum and is responsible for many observed spectral lines in astronomical objects.

2. How is the energy of the photon emitted or absorbed during the n=4 to n=3 transition calculated?

The energy of the photon emitted or absorbed during the n=4 to n=3 transition can be calculated using the Rydberg formula: E = 13.6 eV * (1/3^2 - 1/4^2). This formula takes into account the energy levels of the hydrogen atom and allows for the calculation of the specific energy of the photon.

3. What factors influence the probability of the n=4 to n=3 transition occurring?

The probability of the n=4 to n=3 transition occurring is influenced by a few factors. These include the temperature of the atom, the presence of external electric or magnetic fields, and the number of other atoms or particles in close proximity to the hydrogen atom.

4. How does the n=4 to n=3 transition relate to the Bohr model of the hydrogen atom?

The n=4 to n=3 transition is one of many transitions that occur in the hydrogen atom according to the Bohr model. This model describes the atom as having discrete energy levels, with the n=4 and n=3 levels being two of these levels. The n=4 to n=3 transition occurs when an electron moves from the n=4 level to the n=3 level, releasing or absorbing a photon in the process.

5. Can the n=4 to n=3 transition occur in any other atoms besides hydrogen?

Yes, the n=4 to n=3 transition can occur in other atoms besides hydrogen. However, the energy levels and resulting photon energies will differ from those in hydrogen due to the different atomic structures and electron configurations of these atoms. For example, in helium, the n=4 to n=3 transition corresponds to the release or absorption of a photon in the visible light range, resulting in the observed spectral lines of this element.

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