Question 1

Paper 2Hard10 marks

A monochromatic X-ray photon scatters from an electron that is initially at rest. Model the interaction as a single photon–electron event, with no energy transferred to the rest of the material. Treat the recoiling electron non-relativistically.

Figure 1 shows the geometry and the measured photon wavelengths. The wavelengths are rounded to the nearest 0.00001 nm0.00001\ \mathrm{nm}

xyincident photon, λi=0.08000 nmscattered photon, λs=0.08243 nm90°Oelectron initially at rest

Use h=6.626×10−34 J sh=6.626\times10^{-34}\ \mathrm{J\,s} c=2.998×108 m s−1c=2.998\times10^8\ \mathrm{m\,s^{-1}} and me=9.11×10−31 kgm_e=9.11\times10^{-31}\ \mathrm{kg}

(a)

Calculate the increase in wavelength of the photon.

[1]
(b)

Calculate the kinetic energy transferred to the electron, in J.

[2]
(c)

Determine the speed and direction of the recoiling electron. Give the direction relative to the positive xx-axis.

[4]
(d)

Calculate the electron’s kinetic energy using your result from (c). Comment on whether this is consistent with your answer to (b), taking the precision of the wavelength measurements into account.

[3]

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