Describe what is meant by the de Broglie hypothesis.

(i)     Calculate the kinetic energy of the particle.

(ii)     Determine the de Broglie wavelength of the particle.

all particles have an associated wavelength / OWTTE;

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

(i)     \({E_{\text{K}}}( = 3.2 \times {10^{ - 19}} \times 25 \times {10^3}) = 8.0 \times {10^{ - 15}}{\text{ (J)}}\)\(\,\,\,\)or\(\,\,\,\)50 (keV);

(ii)     use of \({E_{\text{K}}} = \frac{{{p^2}}}{{2m}}\)\(\,\,\,\)and\(\,\,\,\)\(p = \frac{h}{\lambda }\)\(\,\,\,\)or\(\,\,\,\)use of \({E_{\text{K}}} = \frac{1}{2}m{v^2}\)\(\,\,\,\)and\(\,\,\,\)\(p = mv = \frac{h}{\lambda }\);

\(p = 1.0 \times {10^{ - 20}}{\text{ (Ns)}}\);

\(\lambda  = \left( {\frac{h}{p} = } \right){\text{ }}6.6 \times {10^{ - 14}}{\text{ (m)}}\)\(\,\,\,\)or\(\,\,\,\)\(6.5 \times {10^{ - 14}}{\text{ (m)}}\);

Award [3] for a bald correct answer.

The de Broglie hypothesis was sometimes stated poorly and symbols sometimes not defined.

In (i) the kintetic energy was usually correct, but in (ii) far fewer correct answers were seen due to both algebraic and arithmetic errors. A common mistake was to treat the de Broglie wavelength as electromagnetic.