X-ray Production & Minimum Wavelength | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Accelerate electrons, then stop them rapidly

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X-ray production. Heating releases electrons from the cathode. A high accelerating p.d. gives them kinetic energy eV. Their sudden deceleration at the metal target produces X-rays; the shortest possible wavelength satisfies eV = hc/λmin.

Heating the cathode releases electrons by thermionic emission.
A large potential difference accelerates the electrons through the evacuated tube.
The electrons strike a metal target and decelerate rapidly. Some of their energy is emitted as X-ray photons.

Most of the input energy heats the target. The target therefore needs a high melting point and effective cooling (9702/42/F/M/24 Q9(a)(ii)).

One electron sets the photon-energy limit

An electron crossing a potential difference has a maximum kinetic energy of $eV$ . The highest-energy X-ray photon is produced if one electron transfers all of that energy to one photon.

eV=hf_{\max}=\dfrac{hc}{\lambda_{\min}}

\lambda_{\min}=\dfrac{hc}{eV}

Symbols

$e$ = elementary charge (C)
$V$ = accelerating potential difference (V)
$h$ = Planck constant (J s)
$c$ = speed of light in vacuum (m s⁻¹)

Control increased	Immediate change	Exam conclusion
heater current (so tube current increases)	more electrons strike the target each second	greater X-ray intensity; λmin unchanged
accelerating p.d.	more kinetic energy per electron	greater maximum photon energy; smaller λmin

Worked example

Minimum wavelength at 84 kV

eV=1.34\times10^{-14}\ \mathrm{J}

\lambda_{\min}=\dfrac{hc}{eV}

Answer

\lambda_{\min}=1.5\times10^{-11}\ \mathrm{m}

Your turnrelationship check

The accelerating p.d. is doubled while the heater current is unchanged. State what happens to the minimum X-ray wavelength.

Show worked answer

The minimum wavelength halves because it is inversely proportional to the accelerating p.d.