Final answer:
The de Broglie wavelength of an electron confined to the size of a nucleus suggests a high kinetic energy due to the high velocity needed for such confinement, exemplifying principles of quantum mechanics.
Step-by-step explanation:
The question explores the quantum mechanics concept of the de Broglie wavelength of an electron and its implications for the electron's kinetic energy when confined to a space similar in size to that of a nucleus. We know that for an electron to be confined to a nucleus-sized region, which is on the order of 10-15 m, its de Broglie wavelength would also need to be on this order of magnitude or smaller. Using the particle in a box model, we can approximate the ground state energy of an electron in such a tiny confinement.
Since the question states the electron must have a de Broglie wavelength similar to that of the nucleus' diameter, a corresponding high velocity is required, which will result in a significantly high kinetic energy for the electron. For an electron confined to such small dimensions, the uncertainty in position and velocity (according to Heisenberg's uncertainty principle) causes its kinetic energy to be much higher than typical energy differences found between energy levels in atoms.