Question

what is the shape of an atom?

Answer 1

The easy answer is that atoms are not sphericalin shape. Sphere is a solid object, atoms to not have well defined boundaries with "solid cutoffs". Atoms are more like clouds consisting distributions of electrons, neutrons and protons. Atoms, per definition, are electrons + a single nucleus, ie.

Answer 2

he shape and structure of any atom is not rigid as the classical things we observe everyday. To describe a structure, the orbitals around the nucleus, we need to use Schrodinger’s equation. But it's just a mathematical way of describing the fuzzy quantum states of particles, namely how they behave in both space and time. To observe the position of electron at any moment will yield no results related to structure of atom. But now scientists have been able to capture a full quantum state with a tool that can statistically average many measurements over time. This is possible with the help of quantum microscope — a device that uses photoionization microscopy. As hydrogen atom has a single electron, it's pretty easy to observe and compare the structure with its mathematical counterpart.

For more details you can follow the work by Aneta Stodolna of the FOM Institute for Atomic and Molecular Physics (AMOLF) in the Netherlands at Hydrogen Atoms under Magnification: Direct Observation of the Nodal Structure of Stark States

Okay, it's the 2D structure of a hydrogen atom only. As we increase the orbital numbers, the structure will get complicated and those are not yet observed directly, to my knowledge.