This is a good place to start: https://en.wikipedia.org/wiki/Discovery_of_nuclear_fission

There's a few key things that lead to nuclear weapons:

• starting point:

  • know about relativity and mass/energy equivalence
  • observe naturally radioactive elements
  • discover neutrons
  • notice that isotopes exist
    • measure isotopic masses precisely

• realisation: large amounts of energy are theoretically available by rearranging protons/neutrons into things closer to iron (IE:curve of binding energy)

That's not something that can be easily suppressed without suppressing the entire field of nuclear physics.

What else can be hidden?

Assuming there is a conspiracy doing cutting edge nuclear physics and they discover the facts pointing to feasibility of nuclear weapons there are a few suppression options:

• fissile elements? what fissile elements? All we have is radioactive decay.
• Critical mass? You're going to need a building sized lump of uranium.

Discovering nuclear fission was quite difficult. A Nobel prize was awarded partly in error because chemical analysis of fission products were misidentified as transuranic elements.

Presumably the leading labs could have acknowledged that producing transuranic elements was possible through neutron bombardment but kept the discovery of neutron induced fission a secret.

What about nuclear power without nuclear weapons

That's harder. Fudging the numbers on critical mass would require much larger conspiracies. An entire industry would be built on faulty measurement data with true values substituted in key places.

Isotopic separation would still be developed if only for other scientific work (EG:radioactive tracing). Ditto for mass spectroscopy, likely including some instruments capable of measuring heavier elements like uranium isotopes.

Plausibly this would involve lying about some combination of:

• neutrons released during fission (neutrons are somewhat difficult to measure)
• ratio between production of transuranic elements and fission
  • explain observed radiation from fission as transuranic elements, nuclear isomers or something like that.
    • The chemical work necessary to distinguish transuranic elements from fission products is quite difficult.

A nuclear physicist would be better qualified in figuring out something plausible.

My initial thought is that the public would almost certainly not be offered details, but the State would want the existence of the an atomic bomb project generally known. That information would be calculated to intimidate the "enemy" and provide a sense of security for the public.

That, combined with the number of people needed to complete the project, sends the possibility of secrecy firmly out the window.