Wavelengths associated with an electron (${\mathit{\lambda }}_{\mathit{e}}$), proton (${\mathit{\lambda }}_{\mathit{p}}$), and deuteron (${\mathit{\lambda }}_{\mathit{d}}$), all moving with the same speed.
Using de Broglie’s equation: $\mathit{\lambda }=\frac{\mathit{h}}{\mathit{m}\mathit{v}}$
• Since all particles have the same speed (v), their wavelengths are inversely proportional to their masses.
• Electron has the smallest mass, so it has the longest wavelength.
• Deuteron has the highest mass, so it has the shortest wavelength.
Mass relation:
thus,
wavelength relation: ${\mathit{\lambda }}_{\mathit{e}}>{\mathit{\lambda }}_{\mathit{p}}>{\mathit{\lambda }}_{\mathit{d}}$