Changes

==Explanation==

==Explanation==

The lengthening of the wavelength happens when a photon interacts with a free electron in the material. The effect can be calculated along the following lines.

The lengthening of the wavelength happens when a photon interacts with a free electron in the material. The effect can be calculated along the following lines. The derivation requires [[relativity]].

1) '''Conservation of energy''': We assume that before the collision, the electron is nearly at rest, so its kinetic energy is zero: <math>E_e=0</math>.  The photon has an energy of <math>E_{\gamma}= h f</math>, where <math>h</math> is Planck's constant, and <math>f</math> is its initial frequency. After the interaction, the photon's frequency changed to <math>f'</math>, so its energy is now <math>E'_{\gamma} = h f'</math>. The kinetic energy of the electron after the collision is <math>E'_e = \sqrt{p^2_e c^2 + m^2_e c^4} - m^2_e c^2</math>. (Here, <math>m_e</math> is the mass of the electron.)  We get the equation;

1) '''Conservation of energy''': We assume that before the collision, the electron is nearly at rest, so its kinetic energy is zero: <math>E_e=0</math>.  The photon has an energy of <math>E_{\gamma}= h f</math>, where <math>h</math> is Planck's constant, and <math>f</math> is its initial frequency. After the interaction, the photon's frequency changed to <math>f'</math>, so its energy is now <math>E'_{\gamma} = h f'</math>. The kinetic energy of the electron after the collision is <math>E'_e = \sqrt{p^2_e c^2 + m^2_e c^4} - m^2_e c^2</math>. This is the relativistic energy of the [[electron]] minus its rest mass energy, given by [[e=mc^2|E=m²]]. (Here, <math>m_e</math> is the mass of the electron.)  We get the equation;

<center><math> h f  = h f' +\sqrt{p^2_e c^2 + m^2_e c^4} - m_e c^2</math></center>

<center><math> h f  = h f' +\sqrt{p^2_e c^2 + m^2_e c^4} - m_e c^2</math></center>