Respuesta :
ANSWER
[tex]\begin{equation*} 81.78\text{ nm} \end{equation*}[/tex]EXPLANATION
Wavelength of incident X-rays, λ = 2.80 * 10^-10 m
Scattered angle, θ = 37.37°
To find the wavelength of the scattered x-rays, apply the equation for Compton's effect:
[tex]\lambda^{\prime}-\lambda=\frac{h}{m_oc}(1-\cos\theta)[/tex]where h = Planck's constant
λ' = wavelength of the scattered x-rays
Substitute the given values into the equation and solve for λ':
[tex]\begin{gathered} \lambda^{\prime}-2.80*10^{-10}=\frac{6.63*10^{-34}}{1.67*10^{-27}}(1-\cos37.37) \\ \\ \lambda^{\prime}-2.80*10^{-10}=\frac{6.63*10^{-34}}{1.67*10^{-27}}*0.2053 \\ \\ \lambda^{\prime}-2.80*10^{-10}=8.15*10^{-8} \\ \\ \lambda^{\prime}=8.15*10^{-8}+2.80*10^{-10} \\ \\ \lambda^{\prime}=8.178*10^{-8}\text{ m}=81.78\text{ nm} \end{gathered}[/tex]That is the wavelength of the scattered x-rays in nanometers.
