Determine whether the radial functions for the 2s and 2p orbitals of a hydrogen atom (R2,0(r) and R2,1(r)] are eigenfunctions of the Coulombic potential energy operator: V^ = -Ze² /4πϵ₀r. If so, give the eigenvalues. If not, then calculate the expectation values of the average potential energies of an electron in 2s and 2p orbitals of a hydrogen atom. Hints: recall that the volume element in spherical polar coordinates is dv = r2sinθdrdθdΦ. Also, recall that the spherical harmonics are normalized.

In a load, the load is paralel to the shaft. n a. angular n b. thrust n c radial n d. none of the above

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

What are the factors that affect the resistance of a wire?