What is the wavelength of the incident photon?

In summary, the maximum energy transferred to an electron in Compton scattering is 45 keV. To find the wavelength of the incident photon, one must apply conservation of energy and use the equation \lambda_2 - \lambda_1 = h/mc (1 - cos \theta ), where theta is not equal to 90 degrees.
  • #1
roeb
107
1

Homework Statement


If the maximum energy imparted to an electron in Compton scattering is 45 keV. What is the wavelength of the incident photon?


Homework Equations





The Attempt at a Solution



[tex]\lambda_2 - \lambda_1 = h/mc (1 - cos \theta )[/tex]
My first initial thought was to apply conservation of energy.

initial = final

hf + [tex]m_0 c^2[/tex] = [tex]m_0 c^2[/tex] + Ke + hf'
Where Ke = 45 keV (the kinetic energy of the scattered electron).
Since the problem states maximum energy, I thought that this would mean that theta = 90.

I then proceeded to get f - f' = 1.08 x 10^(19) Hz.

Then I was thinking well, since this is a maximum energy, why not say that f' = 0 (all of the photon's energy is absorbed, but then again that isn't really scattering is it?)

Unfortunately, using c = f [tex]\lambda[/tex] I still get the incorrect answer.

Does anyone know what I did incorrectly?

[tex]test[/tex]
 
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  • #2
Hi roeb,

roeb said:

Homework Statement


If the maximum energy imparted to an electron in Compton scattering is 45 keV. What is the wavelength of the incident photon?


Homework Equations





The Attempt at a Solution



[tex]\lambda_2 - \lambda_1 = h/mc (1 - cos \theta )[/tex]
My first initial thought was to apply conservation of energy.

initial = final

hf + [tex]m_0 c^2[/tex] = [tex]m_0 c^2[/tex] + Ke + hf'
Where Ke = 45 keV (the kinetic energy of the scattered electron).
Since the problem states maximum energy, I thought that this would mean that theta = 90.

I believe this is an error. The maximum of the energy transferred to the electron does not occur when theta=90 degrees. Do you see what angle it needs to be instead?
 
  • #3
I would like to clarify that the wavelength of the incident photon cannot be determined solely from the maximum energy imparted to the electron in Compton scattering. This is because the energy of a photon is directly related to its frequency, not its wavelength. The equation E = hf can be used to calculate the energy of a photon, where h is Planck's constant and f is the frequency.

Therefore, to find the wavelength of the incident photon, we would need to know either the frequency or the energy of the photon, in addition to the angle of scattering. The wavelength can then be calculated using the formula \lambda = c/f, where c is the speed of light.

In the given problem, we are only given the maximum energy imparted to the electron in Compton scattering, but we do not know the frequency or the angle of scattering. Without this information, we cannot determine the wavelength of the incident photon.

In conclusion, the question as it is presented does not provide enough information to determine the wavelength of the incident photon. Additional information, such as the frequency or angle of scattering, would be needed to solve the problem.
 

What is the wavelength of the incident photon?

The wavelength of the incident photon refers to the distance between two consecutive peaks or troughs of the photon's electromagnetic wave. It is typically measured in nanometers (nm) or meters (m).

Why is the wavelength of the incident photon important?

The wavelength of the incident photon is important because it determines the properties and behavior of the photon. It also plays a crucial role in how the photon interacts with matter and the type of energy it carries.

How is the wavelength of the incident photon calculated?

The wavelength of the incident photon can be calculated using the equation λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency of the photon's electromagnetic wave.

What is the relationship between wavelength and frequency of an incident photon?

The wavelength and frequency of an incident photon are inversely proportional to each other. This means that when one increases, the other decreases and vice versa. This relationship is described by the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency.

How does the wavelength of the incident photon affect its energy?

The wavelength of the incident photon is directly related to its energy. As the wavelength decreases, the energy of the photon increases. This is known as the inverse relationship between wavelength and energy, which is described by the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency.

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