The correct answer is option 'B' - 3s.

The electron probability distribution refers to the likelihood of finding an electron at a particular location around the nucleus of an atom. In other words, it represents the probability of finding an electron in a given region of space.

Spherically symmetric distribution means that the probability of finding an electron is the same at any point equidistant from the nucleus. This implies that the electron cloud around the nucleus is symmetrical in all directions, resembling a sphere.

Let's understand why the 3s orbital has a spherically symmetric electron probability distribution.

1. Orbitals:
In quantum mechanics, orbitals are mathematical functions that describe the behavior of electrons in an atom. Orbitals are labeled by three quantum numbers: the principal quantum number (n), the angular momentum quantum number (l), and the magnetic quantum number (m).

2. Quantum numbers for the 3s orbital:
For the 3s orbital, the principal quantum number (n) is 3, the angular momentum quantum number (l) is 0, and the magnetic quantum number (m) is 0. These quantum numbers determine the shape, size, and orientation of the orbital.

3. Shape of the 3s orbital:
The 3s orbital is spherical in shape. It is characterized by a single lobe that is centered around the nucleus. The electron density is highest at the nucleus and decreases as you move away from it. The size of the orbital increases with increasing principal quantum number (n), so the 3s orbital is larger than the 1s and 2s orbitals.

4. Spherical symmetry:
The 3s orbital has spherical symmetry because it is only characterized by the principal quantum number (n). It does not have any angular nodes or orientation in space. This means that the probability of finding an electron in the 3s orbital is the same at any point equidistant from the nucleus, resulting in a spherically symmetric electron probability distribution.

In summary, the 3s orbital has a spherically symmetric electron probability distribution because it is spherical in shape and does not have any angular nodes or orientation in space.