Respuesta :
ANSWER
[tex]466,000\text{ pm}[/tex]EXPLANATION
Parameters given:
Energy of X-ray beam = 85.97 MeV
Scattering angle, θ = 100°
To find the wavelength of the x-ray beam, we have to apply the Compton Effect formula:
[tex]\lambda^{\prime}-\lambda=\frac{h}{m_0c}[1-\cos\theta][/tex]where λ' = wavelength of the scattered x-ray
λ = wavelength of the incident x-ray
h = Planck's constant
moc = 1.67 * 10^(-27)
First, we have to find the wavelength of the incident x-ray. To do this, apply the formula for energy:
[tex]\begin{gathered} E=\frac{hc}{\lambda} \\ \\ \lambda=\frac{hc}{E} \end{gathered}[/tex]Therefore, the wavelength of the incident x-ray is:
[tex]\begin{gathered} \lambda=\frac{6.626*10^{-34}*3*10^8}{85.97*10^6*1.6*10^{-19}} \\ \\ \lambda=1.45*10^{-14}\text{ m} \end{gathered}[/tex]Now, substitute the given and obtained values into the equation for Compton's effect and solve for λ':
[tex]\begin{gathered} λ^{\prime}-1.45*10^{-14}=\frac{6.626*10^{-34}}{1.67*10^{-27}}*(1-\cos100) \\ \\ λ^{\prime}-1.45*10^{-14}=\frac{6.626*10^{-34}}{1.67*10^{-27}}*1.174 \\ \\ λ^{\prime}-1.45*10^{-14}=4.66*10^{-7} \\ \\ λ^{\prime}=4.66*10^{-7}+1.45*10^{-14} \\ \\ λ^{\prime}=4.66*10^{-7}\text{ m}=466,000\text{ pm} \end{gathered}[/tex]That is the wavelength of the scattered x-rays.
