Quantised Photon Energy and Compton Scattering

[timmyeatchips]

To back me up with some of my chemistry courses this year, I picked up a quantum mechanics book that looked like it included some fairly simple introductions to quantum principles.
However, in the first chapter it used Compton scattering, the lowering in wavelength of X rays due to collision with atomic electrons, as early evidence for the existence of the photon.

My question is, how does this partial loss of energy fit in with the idea of photon energy being quantised?

 

[humanino]

Welcome Timmy, and please let some chips for everyone

You must first be aware that it is not possible to deviate a photon, but in Compton scattering it looks like it is. Planck earlier used the formula E=h \nu to find the good black-body radiation spectrum, both in infrared and ultra-violet light, and this was the birth of QM. Compton used this formula and the idea that photon is a regular particle, but only in that he applied conservation of energy and momentum as in regular billard game. This allowed him to derive his \lambda_f-\lambda_i=\frac{h}{m_ec}\left (1-\cos(\theta)\right ) that explained Xrays diffraction by crystals.
See hyperphysics for instance.

 

[R0man]

Quantised photon energy is a fundamental concept in quantum mechanics, stating that the energy of a photon is only allowed to take on certain discrete values. This is in contrast to classical physics, where energy can take on any continuous value. Compton scattering, which is the phenomenon of X-ray photons losing energy when they collide with atomic electrons, is a perfect example of this quantisation of energy.

In Compton scattering, the X-ray photons are absorbed by the electrons and then re-emitted with a lower energy. This decrease in energy can be explained by the quantisation of photon energy. The energy of the X-ray photon before the collision is a specific, discrete value. When it collides with the electron, it transfers some of its energy to the electron, resulting in a lower energy photon being emitted. This lower energy photon also has a specific, discrete value, in accordance with the quantisation of photon energy.

This partial loss of energy in Compton scattering is a clear demonstration of the quantised nature of photon energy. It shows that the energy of a photon cannot take on any value, but rather is limited to specific, quantised values. This concept is essential in understanding the behavior of light and matter at the quantum level.

In addition, Compton scattering played a crucial role in providing evidence for the existence of photons. The observed decrease in wavelength of X-rays due to collision with electrons could not be explained by classical wave theory, but it was consistent with the idea of photons as discrete packets of energy. This further supports the concept of quantised photon energy.

In conclusion, the partial loss of energy in Compton scattering is a perfect example of the quantisation of photon energy. It showcases the discrete nature of energy at the quantum level and provides evidence for the existence of photons. Understanding this concept is essential in grasping the fundamental principles of quantum mechanics.