The radial distribution function can be defined in two ways: 4πr²R(r)² and r²R(r)², with the former including a factor of 4π. This discrepancy arises from whether the calculation is for volume or area; the 4π factor is necessary for volume calculations, while the simpler form is used for area. The normalization of the wavefunction, which ensures that the total probability equals one, supports the inclusion of the 4π factor in volume contexts. Understanding the context of the calculation is crucial for determining which expression to use. Proper application of these definitions is essential for accurate quantum mechanical computations.