Final answer:
The question involves concepts from quantum mechanics and uses mathematical constants and symbols such as π and Planck's constant (ħ). It likely pertains to the area of a circle, wave functions, and angular momentum. More context is needed for a complete solution.
Step-by-step explanation:
The question seems to concern a physics or mathematics problem involving angular momentum (L), Planck's constant (ħ), and perhaps the normalization condition for wave functions. The reference to pie seems to be a typo and might refer to the mathematical constant pie (π), especially in conjunction with a squared radius (r2), suggestive of an area of a circle formula (πr2). From the provided snippets of solutions, it appears that quantum mechanical concepts are involved, such as quantized angular momentum, and the use of π and ħ indicates a context of wave functions or orbitals.
The normalization condition mention suggests that the problem is looking for a normalized wave function, which takes the general form A = √(2/L) in some cases, where A is the amplitude of the wave function and L might represent the system's size or some characteristic length. Additionally, the discussion of angular momentum and the equation L = √[l(l + 1)]ħ implies we are dealing with orbital angular momentum in quantum mechanics.
However, without more context or the actual figures mentioned, it's challenging to provide a full step-by-step solution. The quoted fragments suggest a multi-step problem that involves substituting values for angular momentum and perhaps solving for wave function normalization.