Final answer:
Normalization of a wave function in quantum mechanics for a hydrogen atom involves integrating the square modulus of the provided wave function over all space using spherical coordinates to ensure the total probability is one.
Step-by-step explanation:
Normalizing a wave function in quantum mechanics ensures that the total probability of finding a particle within the entire space is equal to one. For the given hydrogen atom wave function φ(r,θ,φ)=rexp(−r/2)sinθe−ᴉφ, we can normalize it by ensuring that the integral of the square modulus of the wave function over all space is equal to one. This involves spherical coordinates (θ, φ) and the radial part (r). Remembering that the volume element in spherical coordinates is dV = r^2 sinθ dr dθ dφ, we integrate the probability density |φ|^2 over the entire space. Given the form of φ, we notice that the integral will involve the provided auxiliary integral for the angular part and for the radial part we make use of the given integral ∫₀∞ x⁴e−˃dx=24. Normalization requires using these integrals to find the constant that will make the integral of the probability density over all space equal to 1.