Question #43686

This question tests the transition from classical to relativistic mechanics in the context of matter waves.

Students commonly fall into the trap of calculating the Q-value ($Q = \Delta m c^2 = 3mc^2$), assigning half of it as classical kinetic energy to each particle ($K = 1.5mc^2$), and then incorrectly applying the classical momentum relation $p = \sqrt{2mK}$.

This leads to the erroneous classical De Broglie wavelength $\lambda = h/\sqrt{3}mc$ and fringe width (Option B).

The blueprint forces the realization that when kinetic energy is comparable to or exceeds rest mass energy, the relativistic energy-momentum invariant $E^2 = (pc)^2 + (mc^2)^2$ must be used to find the correct momentum for the De Broglie wavelength scaling.