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 :

Options

A. A, B, C, D and E
B. A, B and E only
C. B and D only
D. A, C and E only

Answer

To solve the question, we will analyze each statement one by one to determine their correctness.

### Step-by-Step Solution:

1. **Statement A**: "Atoms of each element emit characteristic spectrum."
- This statement is **true**. Each element has a unique electronic structure, which means that when electrons transition between energy levels, they emit or absorb specific wavelengths of light, resulting in a characteristic spectrum. This is the basis for techniques like spectroscopy used to identify elements.

2. **Statement B**: "According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit."
- This statement is also **true**. Bohr proposed that electrons in a hydrogen atom occupy fixed orbits (stationary states) where they do not radiate energy. This concept is fundamental to Bohr's model of the atom.

3. **Statement C**: "The density of nuclear matter depends on the size of the nucleus."
- This statement is **false**. The density of nuclear matter is approximately constant across different nuclei, regardless of their size. While the mass of a nucleus increases with size, the volume also increases, leading to a constant density.

4. **Statement D**: "A free neutron is stable but a free proton decay is possible."
- This statement is **false**. A free neutron is not stable; it has a half-life of about 14 minutes and decays into a proton, an electron, and an antineutrino. Protons are considered stable in isolation under normal conditions and do not decay in the same way.

5. **Statement E**: "Radioactivity is an indication of the instability of nuclei."
- This statement is **true**. Radioactivity occurs when an unstable nucleus seeks to reach a more stable configuration by emitting radiation. Thus, radioactivity is indeed a sign of nuclear instability.

### Summary of Correct Statements:
- Correct statements: A, B, and E.
- Incorrect statements: C and D.

### Final Answer:
The correct answer includes statements A, B, and E.

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