Answer to Question #106432 in Quantum Mechanics for Nikita Koladiya

Question

A photon and an electron each have an energy of .eV100.63 What are their wavelengths? Which of these would you use to probe atomic structures?

Answer 1

Suppose that $E=100.63 keV$

For electron

$\lambda_e=\frac{h}{mv}=\frac{h}{\sqrt{{2mE}}}=\frac{6.62\cdot10^{-34}}{\sqrt{{2\cdot 9.11\cdot10^{-31}\cdot 1.6\cdot10^{-19}\cdot100630}}}=$

$=3.86\cdot10^{-12}m=3.86pm$

For proton

$\lambda_p=\frac{h}{mv}=\frac{h}{\sqrt{{2mE}}}=\frac{6.62\cdot10^{-34}}{\sqrt{{2\cdot 1.67\cdot10^{-27}\cdot 1.6\cdot10^{-19}\cdot100630}}}=$

$=9.03\cdot10^{-14}m\approx0.09pm$

I would use electrons to probe atomic structures.