Describe wave-particle duality in relation to the de Broglie hypothesis.

The electrons were accelerated through a potential difference of 54 V. Show that the associated de Broglie wavelength for the electrons is about \(2 \times {10^{ - 10}}{\text{ m}}\).

The electron detector recorded a large number of electrons at a particular scattering angle \(\theta \). Explain why a maximum in the number of scattered electrons is observed at a particular angle.

a particle with momentum has a wavelength ;

where \(\lambda  = \frac{h}{p}\) and wavelength is \(\lambda \), momentum is \(p\) and Planck’s constant is \(h\);

\(p = \sqrt {2{m_{\text{e}}} \times eV}  = \sqrt {2 \times 9.11 \times {{10}^{ - 31}} \times 1.60 \times {{10}^{ - 19}} \times 54} {\text{ }}( = 3.97 \times {10^{ - 24}}{\text{ kg}}\,{\text{m}}\,{{\text{s}}^{ - 1}})\);

\(\lambda  = \left( {\frac{h}{{\sqrt {2{m_{\text{e}}} \times eV} }} = \frac{{6.63 \times {{10}^{ - 34}}}}{{3.97 \times {{10}^{ - 24}}}} = } \right){\text{ }}1.7 \times {10^{ - 10}}{\text{ m}}\); }

(must see 2+ significant figures to award this mark)

electrons scatter off the periodic structure of the nickel lattice;

separation of ions/atoms is such that diffraction occurs (leading to a maximum in the intensity of scattered electrons);

(a) was usually well answered.

(b)(i) was either well answered or incorrect.

(b)(ii) was very poorly answered.