Chapter 38: Q40P (page 1183)

What is the maximum kinetic energy of electrons knocked out of a thin copper foil by Compton scattering of an incident beam of 17.5 keV x-rays? Assume the work function is negligible.

Short Answer

Expert verified

The maximum energy of electron is 1.1 keV.

Step by step solution

The given data

Compton scattering of an incident beam of 17.5 keV x-rays is done to knock electrons out a thin copper foil

Formula used

Here, $E λ = h c$

Where E is energy

$λ$ is wavelength

h is Plank’s constant

C is speed of light.

Change in the wavelength

Using $h c = 1240 eV \cdot nm$

$E λ = h c λ = \frac{h c}{E} λ = \frac{1240 eV \cdot nm}{17500 eV} = 0.07086 nm$

Maximum Crompton shift occur for $φ = 180 °$ yields

$\begin{matrix} Δ λ = (\frac{h c}{m_{e} c^{2}}) (1 - \cos 180 °) \\ = (\frac{1240 eV \cdot nm}{511 \times 10^{3} eV}) (1 - (- 1)) \\ = 0.00485 nm \end{matrix}$

New photon energy

New photon wavelength $λ^{'}$ is

$λ^{'} = 0.07086 nm + 0.00485 nm = 0.0757 nm$

$\begin{matrix} E^{'} = \frac{h c}{λ^{'}} \\ = \frac{1240 eV \cdot nm}{0.0757 nm} \\ = 1.64 \times 10^{4} eV \end{matrix}$

New photon energy $16.4 keV$

Kinetic energy of electron

Kinetic energy of electron is

$E^{'} - E = 17.5 keV - 16.4 keV = 1.1 keV$

Hence, maximum kinetic energy of electron is $1.1 keV$

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What is the maximum kinetic energy of electrons knocked out of a thin copper foil by Compton scattering of an incident beam of 17.5 keV x-rays? Assume the work function is negligible.

Short Answer

Step by step solution

The given data

Formula used

Change in the wavelength

New photon energy

Kinetic energy of electron

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