91影视

The energy of the photon is,$E=200\text{鈥塳别痴}$

The photon losses is$10\%$,.

The expression to calculate the energy is given as follows.

$E=\frac{hc}{位}$ 鈥�(颈)

Here,h is the plank鈥檚 constant and c is the speed of light.

The expression to calculate the change in the wavelength is given as follows.

$螖位=\frac{h}{mc}(1-cos胃)$ 鈥�(颈颈)

Here,m is the mass of the electron.

The expression to calculate the changes in the photon鈥檚 energy is given as follows.

$螖E\%=\frac{E-E^{\text{'}}}{E}$ 鈥�(颈颈颈)

Here,$E^{\text{'}}$ is the energy after the scattering and is the energy before the scattering.

The energy of the scattered photon is given by,

$E^{\text{'}}=\frac{hc}{{位}^{\text{'}}}$

The energy of the incident photon is given by,

$E=\frac{hc}{位}$

Calculate the change in the photon energy.

Substitute$0.10$for$螖E\%$, $\frac{hc}{{位}^{\text{'}}}$for $E^{\text{'}}$and$\frac{hc}{位}$for E into equation (iii).

$\begin{array}{l}0.10=\frac{\frac{hc}{位}鈭�\frac{hc}{{位}^{\text{'}}}}{\frac{hc}{位}}\\ 0.10=\frac{\frac{1}{位}鈭�\frac{1}{{位}^{\text{'}}}}{\frac{1}{位}}\\ 0.10=\frac{{位}^{\text{'}}鈭�位}{{位}^{\text{'}}}\end{array}$

Substitute $螖位$for ${位}^{\text{'}}鈭�位$into above equation.

$\begin{array}{c}0.10=\frac{螖位}{{位}^{\text{'}}}\\ 螖位=0.10{位}^{\text{'}}\\ 螖位=0.10(位+螖位)\\ 螖位=\frac{位}{9}\end{array}$

Substitute $位/9$for $螖位$into equation (ii).

$\begin{array}{l}\frac{位}{9}=\frac{h}{mc}(1鈭�\cos 胃)\\ 位=\frac{9h}{mc}(1鈭�\cos 胃)\end{array}$

Substitute$hc/E$for $位$into above equation.

$\begin{array}{c}\frac{hc}{E}=\frac{9h}{mc}(1鈭�\cos 胃)\\ \frac{c}{E}=\frac{9}{mc}(1鈭�\cos 胃)\\ 1=\frac{9E}{m{c}^2}(1鈭�\cos 胃)\\ 1鈭�\cos 胃=\frac{m{c}^2}{9E}\end{array}$

Solve further as,

role="math" localid="1663146814795" $\begin{array}{c}\cos 胃=1鈭�\frac{m{c}^2}{9E}\\ 胃={\cos }^{鈭�1}\left(1鈭�\frac{m{c}^2}{9E}\right)\end{array}$

Substitute $511\text{鈥塳别痴}$for $m{c}^2$and $200\text{鈥塳别痴}$for E into above equation.

$\begin{array}{l}胃={\cos }^{鈭�1}\left(1鈭�\frac{511\text{鈥块别惫}}{9脳200\text{鈥块别惫}}\right)\\ 胃={\cos }^{鈭�1}\left(0.7161\right)\\ 胃=44.2掳\end{array}$

Hence the required value of the angle is.$44.2掳$