Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• In this question you will estimate the total energy of a helium atom. (a) What would be the total energy of a helium atom (in its ground state) in the approximation where you ignore completely the electrostatic force between the two electrons? [Hint: In this approximation you can treat each electron separately as if it were in a hydrogen-like ion. The total energy is just the sum of the two separate energies.] (b) Your answer in part (a) should be negative (indicating that the system is bound) and too negative since you ignored the positive potential energy due to the repulsion between the two electrons. To get a rough estimate of this additional potential energy, imagine the electrons to be in the first Bohr orbit, with radius aB/2 (the appropriate radius for a hydrogen-like ion with Z = 2). To minimize their energy, the two electrons would move around the same circular orbit, always on opposite sides of the nucleus, a distance aB apart. Use this semiclassical model to estimate the potential energy of the two electrons. Combine this with your answer to part (a) to estimate the total energy of the He atom. Compare with the observed value of −79.0 eV.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.