All Problems

Wave Properties of particles. Schrodinger Equation.

Problem 6.55

Derive the expression for a de Broglie wavelength λ\lambda of a relativistic particle moving with kinetic energy T.T . At what values of TT does the error in determining λ\lambda using the non-relativistic formula not exceed 1%1 \% for an electron and a proton?

Reveal Answer
 6.55. λ=2πℏ/2mT(1+T/2mc2),T⩽4mc2Δλ/λ=20.4keV (for  \text { 6.55. } \lambda=2 \pi \hbar / \sqrt{2 m T\left(1+T / 2 m c^{2}\right)}, T \leqslant 4 m c^{2} \Delta \lambda / \lambda=20.4 \mathrm{keV} \text { (for } an electron) and 37.5MeV37.5 \mathrm{MeV} (for a proton).
Prev
Next