Instructions for Homework Problem #30-b

    On homework problem #30(b) you are asked to find the uncertainty in the kinetic energy of a helium atom after having calculated the uncertainty in its momentum.  Since this is an atom in a very cold, solid environment, its motion will be slow and relativistic equations are not needed.  Its kinetic energy will be simply K = p² / (2m) from which it follows that ΔK=pΔp/m.  The problem is that you know Δp, but not p.  However since the atom is oscillating around a fixed mean position, its mean component of momentum, in any direction, will be zero as it oscillates between positive and negative values.  Its average kinetic energy however will not be zero as it will be positive whether the momentum is positive or negative.  Hence take   ΔK to be ΔK= Δp² / 2m. This should give you the correct answer!