Answer to Question #329223 in Quantum Mechanics for Ayesha

Question

for small uncertainty in the measurement of position of a particle, the wavelength of the incident light should be :

Small

Large

Average

Doesn't depend on wavelength

Answer 1

The wavelength should be small.

According to the Heisenberg's uncertainty principle, the uncertainty in position $\Delta x$ is inversely proportional to the uncertainty in speed $\Delta v$. Thus, in order to make $\Delta x$ small, we should make $\Delta v$ big (disturb particle with a radiation of great energy). The energy of radiation is inversely proportional to its wavelength. Thus, in order to obtain greater energy one should choose smaller wavelength.