Wavelengths of photon

In summary, the conversation is about calculating the value of k for a hydrogen atom transition from the k state to the n = 1 state with a wavelength of 94.8 nm. The equation used is 1/lambda = 1.97x10^7(1/1^2-1/k^2), and the calculated value for k is 5. The individual also had a question about the energy of transition and the confusion between absorption and emission of energy. The expert clarified that the transition energy is 13.1eV, not 1.31eV, and explained that the photon absorbs energy when its energy is equal to the energy of transition.
  • #1
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Homework Statement



The wavelength of the photon emitted when a hydrogen atom undergoes a transition from the k state to the n = 1 state is around 94.8 nm. How much is k?

Homework Equations



1/lambda= 1.97x10^7(1/1^2-1/k^2)

The Attempt at a Solution



1/9.48x10^-8=1.097x10^7(1-1/k^2)
10548523,71=1.097x10^7(1-1/k^2)
.9615791437=1-1/k^2
-.03384208563=-1/k^2
26.02753028=k^2
k=5.1 i thought it had to be an integer? do i just round off?

and I am also a bit confused because when i get the energy of transition= hc/lambda, it is equal to 1.31, but (energyK-energyN=energy of transition) .544-13.6= is not even close to 1.31 and i thought it was supposed to equal 1.31 (hf, energy transition) or is that only when the photon absorbs, :/ a bit confused help out please
 
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  • #2
stickplot said:

Homework Statement



The wavelength of the photon emitted when a hydrogen atom undergoes a transition from the k state to the n = 1 state is around 94.8 nm. How much is k?

Homework Equations



1/lambda= 1.97x10^7(1/1^2-1/k^2)

The Attempt at a Solution



1/9.48x10^-8=1.097x10^7(1-1/k^2)
10548523,71=1.097x10^7(1-1/k^2)
.9615791437=1-1/k^2
-.03384208563=-1/k^2
26.02753028=k^2
k=5.1 i thought it had to be an integer? do i just round off?

Yes. [itex]k=5[/itex].

and I am also a bit confused because when i get the energy of transition= hc/lambda, it is equal to 1.31, but (energyK-energyN=energy of transition) .544-13.6= is not even close to 1.31 and i thought it was supposed to equal 1.31 (hf, energy transition) or is that only when the photon absorbs, :/ a bit confused help out please

You miscalculated. The transition energy is 13.1eV, not 1.31eV.
 
  • #3
o ok.
stupid me i see what i did now.
and btw
how do you know when a photon is absorbing energy?
is it when the photon energy is the same to the energy transition? but I am kind of confused because i thought they were always equal to each other
 

1. What is a photon?

A photon is a fundamental particle of light that carries energy and has no mass. It behaves both as a wave and a particle, and is the basic unit of light and other forms of electromagnetic radiation.

2. How are wavelengths of photons measured?

Wavelengths of photons are measured in units of length, typically nanometers (nm) or meters (m). This can be done using a spectrometer, which separates the different wavelengths of light in a spectrum.

3. Why do different photons have different wavelengths?

Photons have different wavelengths because they have different amounts of energy. The wavelength of a photon is inversely proportional to its energy, meaning that higher energy photons have shorter wavelengths and lower energy photons have longer wavelengths.

4. How do wavelengths of photons affect their interaction with matter?

The wavelength of a photon determines its frequency and energy, which in turn affects how it interacts with matter. For example, shorter wavelength photons (such as X-rays) have higher energy and can penetrate deeper into matter, while longer wavelength photons (such as radio waves) have lower energy and are easily absorbed.

5. Can the wavelength of a photon change?

Yes, the wavelength of a photon can change through various processes such as absorption, emission, and scattering. These processes can alter the energy and direction of the photon, resulting in a change in its wavelength.

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