91影视

The wavelength of light $位=10\mathrm{pm}$.

Collision of electron and photon is head therefore$蠒={180}^0$

Photon Energy

The energy that a single photon carries is known as photon energy. Energy is inversely correlated with wavelength because it is directly proportional to the electromagnetic frequency of the photon.

Photon energy of light can be given as

$E=\frac{hc}{位}$

Where $h$is plank constant, $v$is the velocity of light, and $位$is the wavelength

We know $hc=1240nm路eV$

Substituting the values

$\begin{array}{rcl}E& =& \frac{1240nm路eV}{10脳{10}^{-3}nm}\\ & =& 124KeV\end{array}$

Hence the photon energy of the light is $124KeV$.

As we know the energy gained by the Electron must be equal to the decrease in energy of the photon

So, the decrease in energy of the photon can be given as

$鈭�E=鈭�\left(\frac{hc}{位}\right)$

Since $h$and $c$are constant

Therefore,

$\begin{array}{rcl}鈭�E& =& hc\left(\frac{1}{位}-\frac{1}{位+鈭�位}\right)\\ & =& \frac{hc}{位}\left(\frac{鈭�位}{位+鈭�位}\right)\\ & =& \frac{E}{1+{\displaystyle \raisebox{1ex}{$位$}\!\left/ \!\raisebox{-1ex}{$鈭�位$}\right.}}\\ & =& \frac{E}{1+{\displaystyle \raisebox{1ex}{$位$}\!\left/ \!\raisebox{-1ex}{${位}_c\left(1-\cos 蠒\right)$}\right.}}\end{array}$

We know in the head-on collision$蠒={180}^{鈭�}$

Now substituting the values

$\begin{array}{rcl}鈭�\mathrm{E}& =& \frac{\mathrm{E}}{1+{\displaystyle \raisebox{1ex}{$\mathrm{位}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{位}}_{\mathrm{c}}$}\right.}\left(1-\mathrm{肠辞蝉蠒}\right)}\\ & =& \frac{124\mathrm{KeV}}{1+{\displaystyle \raisebox{1ex}{$10\mathrm{pm}$}\!\left/ \!\raisebox{-1ex}{$243\mathrm{pm}$}\right.}\left(1-\cos {180}^{鈭�}\right)}\\ & =& 40.5\mathrm{KeV}\end{array}$

Hence the energy imparted by a photon to an electron in a head-on collision is $40.5\mathrm{KeV}$

The energy imparted by a photon to an electron in a head-on collision is $40.5\mathrm{KeV}$

This is very high energy.

According to the above results, we can conclude that

With the energy supplied to the electron by the photon, the electron would have been thrown out of its orbit, making it impossible to find an atomic electron with such high energy.