Question 20N.2.HL.TZ0.b(ii)

The de Broglie wavelength $\lambda$ of a particle accelerated close to the speed of light is approximately

$\lambda \approx \frac{hc}{E}$

where $E$ is the energy of the particle.
A beam of electrons of energy $4.2\times {10}^8 \mathrm{eV}$ is produced in an accelerator.

The electron beam is used to study the nuclear radius of carbon-12. The beam is directed from the left at a thin sample of carbon-12. A detector is placed at an angle $\theta$ relative to the direction of the incident beam.

The graph shows the variation of the intensity of electrons with $\theta$. There is a minimum of intensity for $\theta ={\theta }_0$.