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Chapter 3: Q30E (page 94)

A typical ionization energy - the energy needed to remove an electron—for the elements is 10 eV. Explain why the energy binding the electron to its atom can be ignored in Compton scattering involving an X-ray photon with wavelength about one-tenth of a nanometer

Short Answer

Expert verified

The energy binding the electron to its atom can be ignored because the energy of the photon is much greater than the binding

Step by step solution

01

Step.1: Concept Introcucution

We consider the energy of a photon E in terms of wavelength λas,

E=hcλ

Where hc = 1240 nm, E is energy, h is Planck’s constant, and speed of light is c

Hence,

E=(1240λnm)eV………………(1)

02

Step.2: Calculation of energy

Given that the photon wavelength is110thofnm

Use equation (1) and substitute the values,

E=1240110nmeV=12400eV

03

Step.3: Comparison with the binding energy

The ionization energy needed for an electron will be the same as the typical binding energy required in a Compton scattering which is given to be 10 eV.

Comparing this with the energy of a photon which is calculated as 12400 eV, the photon energy is orders of magnitude higher than the binding energy of 10 eV. Hence it can be ignored in Compton scattering.

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