Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

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.

•• Find the electric field at r = aB in the 1s state of a hydrogen atom. Compare with the breakdown field of dry air, about 3 × 106V/m. [Hint: Use Gauss’s law; treat the atomic electron as a static charge distribution with charge density ρ(r) = −e|ψ(r)|2; and use the result of Problem 1.]

Problem 1

••• The probability of finding the electron in the region . What is the probability that a 1s electron in hydrogen would be found outside the Bohr radius (r > aB)?