JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Modern Physics

Each element has its own set of energy levels, so the photons it emits form a spectrum characteristic of that element, and this statement is true.
Bohr's postulate does place the electron of a hydrogen atom in stationary orbits in which it revolves without radiating, so this statement is true.
The nuclear radius obeys $R=R_0{A}^{1/3}$, so the nuclear volume is proportional to the mass number and the density $\frac{A{m}_N}{\frac{4}{3}\pi R_0^{3}A}$ is the same for every nucleus; the statement that nuclear density depends on size is false.
A free neutron is unstable and decays with a mean life of about $15$ minutes into a proton, an electron and an antineutrino, while a free proton is stable, so the statement reverses the facts and is false.
Radioactivity is spontaneous decay, which a nucleus undergoes only because it is unstable, so this statement is true.
The true statements are that atoms of each element emit a characteristic spectrum, that an electron in a hydrogen atom revolves in a stationary orbit, and that radioactivity indicates instability of nuclei.