Q.State de Broglie's hypothesis about the wave nature of matter, and write the formula for the de Broglie wavelength of a particle of mass $m$ moving with speed $v$.

The hypothesis. Louis de Broglie proposed, in 1924, that since radiation (ordinarily a wave) shows particle-like behaviour (the photon, with momentum $p=h/\lambda$), matter (ordinarily made of particles) should, by the same symmetry, show wave-like behaviour -- with a definite wavelength associated with any moving particle of matter (Section 11.9).

The formula. For a particle of mass $m$ moving with speed $v$ (momentum $p=mv$), the de Broglie wavelength is

$\lambda = \frac{h}{p} = \frac{h}{mv}$ …

State the symmetry argument (radiation shows particle behaviour, so matter should show wave behaviour), then give …

• Writing the formula with momentum $p$ replaced incorrectly, e.g. $\lambda=h\,mv$ instead of $\lambda=h/mv$ -- wavelength is INVERSELY related to momentum, a faster/heavier particle has a SHORTER wavelength. …