Problem

The ψ2,1,0 state—the 2p state in which mℓ = 0—has most of its probability density along th...

The ψ2,1,0 state—the 2p state in which m = 0—has most of its probability density along the z-axis, and so it is often referred to as a 2pz state. To allow its probability density to stick out in other ways, and thus facilitate various kinds of molecular bonding with other atoms, an atomic electron may assume a wave function that is an algebraic combination of multiple wave functions open to it. One such "hybrid state" is the sum ψ2,1,+1+ ψ2,1,-1 (Note: Because the Schrödinger equation is a linear differential equation, a sum of solutions with the same energy is a solution with that energy. Also, normalization constants may be ignored in the following questions.)

(a) Write this wave function and its probability density in terms of /; B, and < b. (Use the Etiler formula to simplify your result.)

(b) In which of the following ways does this state differ from its parts (i.e., ψ2,1 +1 and ψ2,1 -1) and from the 2pz state: Energy? Radial dependence of its probability density? Angular dependence of its probability density?

(c) This state is often referred to as the 2px. Why?

(d) How might we produce a 2py state?

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