For a given single-electron state, the energy is one-ninth of the ground-state energy, the orbital angular momentum has magnitude 6h, and the spin and orbital angular momenta are as nearly aligned as possible. a) give the spectroscopic notation for this state, b) how many m values are there for this state?

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .

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