 Solution

ID: past-exam-of-the-short-options-paper-of-the-physics-prelims-of-the-university-of-oxford/2021/s03/2/d/solution

An electron accelerated from negligible initial kinetic energy through

V

gains

e V

. The largest possible single photon energy in an X-ray tube is this entire kinetic energy, so the Duane-Hunt law gives

λ_{m i n} = \frac{h c}{e V} = \frac{1239.841984 eV nm}{25000 eV} = 0.0496 nm = 4.96 \times 1 0^{- 11} m .

The massive anode can absorb the required recoil momentum with negligible recoil energy; most actual events produce lower-energy bremsstrahlung photons. The acceleration energy

e V

is valid without approximating the electron speed nonrelativistically.

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