This study addresses the challenging problem of active view selection and uncertainty quantification within the domain of Radiance Fields. Neural Radiance Fields (NeRF) have greatly advanced image rendering and reconstruction, but the cost of acquiring images poses the need to select the most informative viewpoints efficiently. Existing approaches depend on modifying the model architecture or hypothetical perturbation field to indirectly approximate the model uncertainty. However, selecting views from indirect approximation does not guarantee optimal information gain for the model. By leveraging Fisher Information, we directly quantify observed information on the parameters of Radiance Fields and select candidate views by maximizing the Expected Information Gain~(EIG). Our method achieves state-of-the-art results on multiple tasks, including view selection, active mapping, and uncertainty quantification, demonstrating its potential to advance the field of Radiance Fields. Our method with the 3D Gaussian Splatting backend could perform view selections at 70~fps.