Consider the following statements :
A. Atoms of each element emit characteristics spectrum.
B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
C. The density of nuclear matter depends on the size of the nucleus.
D. A free neutron is stable but a free proton decay is possible.
E. Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below :

Solution

Physics sir · 4 steps

Check each statement on its own: two of them flip the truth about nuclei, and that settles it.

1. Spectra and Bohr. Every element has its own set of energy levels, so its atoms emit a characteristic line spectrum, so A is true. Bohr's postulate says the electron moves in certain allowed stationary orbits without radiating, so B is true.
2. Nuclear density. Nuclear radius grows as R = R₀ A^(1/3), so the volume is proportional to A. Mass is also proportional to A, so the density comes out the same for every nucleus. C is false.

   ρ = (A m)/(4/3π R₀³ A) = 3m/(4π R₀³)

3. Neutron and proton. It is the other way round. A free neutron decays, n → p + e⁻ + ν̄, with a half-life of about 10 minutes, while a free proton is stable. D is false. Radioactivity happens because an unstable nucleus moves towards a more stable one, so E is true.
4. So. Only A, B and E are correct, which is option (b).

The idea to keep. Nuclear density is the same for every nucleus because R ∝ A^(1/3) makes volume grow in step with mass. And remember: the free neutron decays, the free proton does not.

Answer from the NTA final answer key. Solution by PrepWiser.