if you took plain neutrons, and put them in a bottle would a bottle full of neutrons weigh less than a bottle of bear protons with no electrons arround?
Thermal neutrons, which are not sensitive to the Coulomb forces in atoms or to the Pauli exclusion principle (except inside nuclei), will diffuse through the bottle walls until they are captured by nuclei that usually go through (n,gamma) reactions. Sometimes they go through (n,alpha) reactions like neutron capture on boron-10. Protons, which are repelled by other other protons or by nuclei, will stop in the bottle walls and capture electrons from the other nuclei. Hydrogen atoms, being small, can diffuse into the bottle walls (or back into the gas as hydrogen) and cause hydrogen embrittlement, especially in steels. This is a concern in the development of the hydrogen economy. To get a sense of the density of a proton gas, it is now possible to buy capacitors that hold a Coulomb of (electron) charge. But a mole (gram molecular weight) of protons contains 96,000 Coulombs of charge.