The eigenfunctions of the hydrogen atom corresponding to maximal angular mo- mentum (n - 1) are п-1 2 2r er/na ym(0, vал-1m (т, 0, ф). n-1 (2n)! \na, па 9,9 where a is the bohr radius. for these states, find the position of the maximum of the probability density wnlm= r2|nim2 with respect to the radial coordinate r, and calculate the expectation value (r)

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Abag of potato chips contains 2.00 l of air when it is sealed at sea level at a pressure of 1.00 atm and a temperature of 20.0 deg c. what will be the volume of the air in the bag if you take it with you, still sealed, to the mountains where the temperature is 7.00 deg c and atmospheric pressure is 70.0 kpa? assume that the bag behaves like a balloon and that the air in the bag is in thermal equilibrium with the outside air.

Atruck driver is attempting to deliver some furniture. first, he travels 8 km east, and then he turns around and travels 3 km west. finally, he turns again and travels 13 km to his destination. what is the drivers total displacement?