Mastering Physics: The de Broglie Relation for Relativistic Particles

The de Broglie relation is valid for particles moving with relativistic speed, as long as the relativistic momentum is used in the de Broglie formula.

Part A
Suppose that, for a high-energy experiment to probe the structure of protons, you need electrons with de Broglie wavelength of . What total energy (including rest energy) would these electrons have?

Express your answer in joules to three significant figures.

ANSWER:	= 1.99×10−9

Notice that the necessary energy is more than four orders of magnitude greater than the rest energy of the electron. This situation, when the speed of the electrons is fairly close to the speed of light, is known as the extreme relativistic regime.