Question

The change in wavelength between an incident X-ray and a Compton scattered X-ray is $\Delta\lambda = \frac{h}{m_0c}(1-\cos\theta)$ where h is Plank's constant, $m_0$ is the rest mass of the ejected electron, $\theta$ is the scattered angle with respect to the initial trajectory and c is the speed of light. Derive an expression for the energy of the scattered X-ray $E' = \frac{E}{1 + \frac{E}{m_0c^2}(1-\cos\theta)}$

          The change in wavelength between an incident X-ray and a
Compton scattered X-ray is
$\Delta\lambda = \frac{h}{m_0c}(1-\cos\theta)$
where h is Plank's constant, $m_0$ is the rest mass of the
ejected electron, $\theta$ is the scattered angle with respect to
the initial trajectory and c is the speed of light.
Derive an expression for the energy of the scattered X-ray
$E' = \frac{E}{1 + \frac{E}{m_0c^2}(1-\cos\theta)}$

The change in wavelength between an incident X-ray and a
Compton scattered X-ray is
Δλ = (h)/(m0c)(1-cosθ)
where h is Plank's constant, m0 is the rest mass of the
ejected electron, θ is the scattered angle with respect to
the initial trajectory and c is the speed of light.
Derive an expression for the energy of the scattered X-ray
E' = (E)/(1 + (E)/(m0c^2)(1-cosθ))

Added by Encarnacion S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Taniya Khandelwal

Step 1

We know that the energy of a photon is given by E = hc/λ, where h is Planck's constant and c is the speed of light. Show more…

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The change in wavelength between an incident X-ray and a Compton scattered X-ray is Î”Î» = Î»' - Î», where h is Planck's constant, m0 is the rest mass of the ejected electron, Î¸ is the scattered angle with respect to the initial trajectory, and c is the speed of light. Derive an expression for the energy of the scattered X-ray. HINT: Use Î”Î» = Î»' - Î» and E = hc/Î». The change in wavelength between an incident X-ray and a Compton scattered X-ray is Î”Î» = -Î» * cosÎ¸, where h is Planck's constant, m0 is the rest mass of the ejected electron, Î¸ is the scattered angle with respect to the initial trajectory, and c is the speed of light. Derive an expression for the energy of the scattered X-ray: E = E' / (1 + (1 - cosÎ¸) * m0 * c)