Chemistry

This problem combines the wave nature of light used to observe the electron with Heisenberg's uncertainty principle. When you use short-wavelength photons to locate an electron precisely, you're limited by diffraction—the position uncertainty is roughly half the wavelength. The key insight is that this tight position constraint forces a large momentum uncertainty: the more precisely you know where the electron is, the less you can know about how fast it's moving. Use the uncertainty principle $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$ to find the minimum momentum spread.

This problem combines the wave nature of light used to observe the electron with Heisenberg's uncertainty principle. When you use short-wavelength photons to locate an electron precisely, you're limited by diffraction—the position uncertainty is roughly half the wavelength. The key insight is that this tight position constraint forces a large momentum uncertainty: the more precisely you know where the electron is, the less you can know about how fast it's moving. Use the uncertainty principle $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$ to find the minimum momentum spread.