Why would using gamma rays to locate an electron affect its momentum?

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Werner Karl Heisenberg sits at a desk in a suit with his hands folded, bookshelves in the background. — Werner Heisenberg Werner Heisenberg.

To measure the position of an electron using a microscope, one must illuminate it with light. According to the Heisenberg uncertainty principle, the precision of this position measurement is limited by the wavelength of the light used; to achieve greater precision, one must use light with a shorter wavelength, such as gamma rays.

However, this process introduces a disturbance to the electron's momentum. Because light exhibits wave-particle duality, the gamma rays act as photons that collide with the electron. This interaction, known as the Compton effect, causes the electron to recoil in a statistically random direction.

The momentum transferred to the electron during this collision is proportional to the momentum of the photon, which is inversely proportional to its wavelength. Consequently, using shorter-wavelength gamma rays to pinpoint the electron's position more accurately results in a larger, more unpredictable change in the electron's momentum, thereby decreasing the precision with which that momentum can be known.1