The orbitals nearest to the nucleus are the ones with lower principal quantum numbers (n) and lower azimuthal quantum numbers (l). In this case, we are comparing orbitals with the same principal quantum number (n = 3) but different azimuthal quantum numbers.
The azimuthal quantum number (l) determines the shape of the orbital. The order of increasing energy and distance from the nucleus for orbitals with the same principal quantum number (n) is as follows:
s-orbital: It has l = 0 and is spherical in shape. In this case, the 3s orbital is closest to the nucleus among the options you provided.
p-orbital: It has l = 1 and is dumbbell-shaped. The 3p orbital is farther from the nucleus compared to the 3s orbital.
d-orbital: It has l = 2 and is more complex in shape. The 3d orbital is further from the nucleus compared to the 3p orbital.
In summary, the 3s orbital is the closest to the nucleus among the options you provided.