The solution to the t-i schr¨odinger equation for hydrogen-like atoms is of the form ψnℓmℓ (r, θ, φ) = cnℓmℓrnℓ(r)y mℓ ℓ (θ, φ) consider the first excited state, n = 2, with ℓ = mℓ = 0, so the wave function takes the form ψ200 = c200 2 − zr a0 e −zr/2a0 if the value of the constant c200 is given by c200 = 1 √ 32π z a0 3/2 for this state (n = 2, ℓ = 0, mℓ = 0) in hydrogen, find the values and evaluate at r = a0 for each of the following: (a) (b) |ψ| 2 , (c) the radial probability density p(r). give your answers in terms of a0