The diffused shape of f orbitals can be attributed to two main factors: the principal quantum number and the azimuthal quantum number (l).
(1) The principal quantum number indicates the energy level of the electron. As the value of n increases, the electron spends more time farther away from the nucleus, resulting in a more diffused distribution of electron density.
(2) The azimuthal quantum number (l) determines the shape of the orbital. For f orbitals, the value of l is 3, which means there are seven possible f orbitals (l=3, m_l = -3, -2, -1, 0, 1, 2, 3). These orbitals have intricate shapes with multiple nodes and lobes that contribute to their diffused nature.
Furthermore, the f orbitals have higher energy compared to the s, p, and d orbitals. Their energy level and spatial extent make them less likely to be found closer to the nucleus, resulting in more diffuse electron distribution.