De Broglie wavelength কী?

Example 34.16 (Why you never diffract)

An electron accelerated through $100\,\mathrm{V}$ has $E_k = 1.60 \times 10^{-17}\,\mathrm{J}$, $p = \sqrt{2m_e E_k} = 5.4 \times 10^{-24}\,\mathrm{kg}\,\mathrm{m}/\mathrm{s}$, so $\lambda \approx 0.12\,\mathrm{nm}$ — the spacing of atoms in a crystal, which therefore acts as its double slit. A $58\,\mathrm{g}$ tennis ball at $25\,\mathrm{m}/\mathrm{s}$: $\lambda = 6.63\times10^{-34}/1.45 \approx 4.6 \times 10^{-34}\,\mathrm{m}$, some $10^{19}$ times smaller than a nucleus — no slit will ever show it fringing. $h$ is so small that quantum graininess surfaces only at the atom’s scale.

Example 34.17 (The electron microscope)

Diffraction forbids resolving detail much smaller than the wavelength used (Chapter 22): visible light stops near $0.5\,\text{µ}\mathrm{m}$. Electrons at $10\,\mathrm{kV}$ have $\lambda \approx 12\,\mathrm{pm}$ — tens of thousands of times shorter: electron microscopes image viruses, cell machinery, even single atoms. The matter wave handed physics a new eye.